Abstract and Applied Analysis Articles (Project Euclid)
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The latest articles from Abstract and Applied Analysis on Project Euclid, a site for mathematics and statistics resources.en-usCopyright 2010 Cornell University LibraryEuclid-L@cornell.edu (Project Euclid Team)Thu, 05 Aug 2010 15:41 EDTMon, 01 Nov 2010 10:13 EDThttp://projecteuclid.org/collection/euclid/images/logo_linking_100.gifProject Euclid
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Convergence Theorem Based on a New Hybrid Projection Method for Finding a Common Solution of Generalized Equilibrium and Variational Inequality Problems in Banach Spaces
http://projecteuclid.org/euclid.aaa/1267538585
<strong>Siwaporn Saewan</strong>, <strong>Poom Kumam</strong>, <strong>Kriengsak Wattanawitoon</strong><p><strong>Source: </strong>Abstr. Appl. Anal., Volume 2010, 25 pages.</p><p><strong>Abstract:</strong><br/>
The purpose of this paper is to introduce a new hybrid projection method for finding a common element of the set of common fixed points of two relatively quasi-nonexpansive mappings, the set of
the variational inequality for an $\alpha$ -inverse-strongly monotone, and the set of solutions of the generalized equilibrium problem in the framework of a real Banach space. We obtain a strong convergence theorem for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach space. Base on this result, we also get some new and interesting results. The results in this paper generalize, extend, and unify some well-known strong convergence results in the literature.
</p>projecteuclid.org/euclid.aaa/1267538585_Thu, 05 Aug 2010 15:41 EDTThu, 05 Aug 2010 15:41 EDTAntinormal Weighted Composition Operatorshttp://projecteuclid.org/euclid.aaa/1481943738<strong>Dilip Kumar</strong>, <strong>Harish Chandra</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2016, 5 pages.</p><p><strong>Abstract:</strong><br/> Let ${l}^{\mathrm{2}}={L}^{\mathrm{2}}(\mathbb{N},\mu )$ , where $\mathbb{N}$ is set of all positive integers and $\mu $ is the counting measure whose $\sigma $ -algebra is the power set of $\mathbb{N}$ . In this paper, we obtain necessary and sufficient conditions for a weighted composition operator to be antinormal on the Hilbert space ${l}^{\mathrm{2}}$ . We also determine a class of antinormal weighted composition operators on Hardy space ${H}^{\mathrm{2}}(\mathbb{D})$ . </p>projecteuclid.org/euclid.aaa/1481943738_20161216220306Fri, 16 Dec 2016 22:03 ESTHyperplanes That Intersect Each Ray of a Cone Once and a Banach Space Counterexamplehttp://projecteuclid.org/euclid.aaa/1481943739<strong>Chris McCarthy</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2016, 7 pages.</p><p><strong>Abstract:</strong><br/> Suppose $C$ is a cone contained in real vector space $V$ . When does $V$ contain a hyperplane $H$ that intersects each of the 0-rays in $C\setminus \{\mathrm{0}\}$ exactly once? We build on results found in Aliprantis, Tourky, and Klee Jr.’s work to give a partial answer to this question. We also present an example of a salient, closed Banach space cone $C$ for which there does not exist a hyperplane that intersects each 0-ray in $C\setminus \{\mathrm{0}\}$ exactly once. </p>projecteuclid.org/euclid.aaa/1481943739_20161216220306Fri, 16 Dec 2016 22:03 ESTA Note on First Passage Functionals for Lévy Processes with Jumps of Rational Laplace Transformshttp://projecteuclid.org/euclid.aaa/1481943740<strong>Djilali Ait-Aoudia</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2016, 8 pages.</p><p><strong>Abstract:</strong><br/> This paper investigates the two-sided first exit problem for a jump process having jumps with rational Laplace transform. The corresponding boundary value problem is solved to obtain an explicit formula for the first passage functional. Also, we derive the distribution of the first passage time to two-sided barriers and the value at the first passage time. </p>projecteuclid.org/euclid.aaa/1481943740_20161216220306Fri, 16 Dec 2016 22:03 ESTQuasi-Hyperbolicity and Delay Semigroupshttp://projecteuclid.org/euclid.aaa/1481943741<strong>Shard Rastogi</strong>, <strong>Sachi Srivastava</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2016, 6 pages.</p><p><strong>Abstract:</strong><br/> We study quasi-hyperbolicity of the delay semigroup associated with the equation ${u}^{\mathrm{\prime }}(t)=Bu(t)+\mathrm{\Phi }{u}_{t}$ , where ${u}_{t}$ is the history function and $(B,D(B))$ is the generator of a quasi-hyperbolic semigroup. We give conditions under which the associated solution semigroup of this equation generates a quasi-hyperbolic semigroup. </p>projecteuclid.org/euclid.aaa/1481943741_20161216220306Fri, 16 Dec 2016 22:03 ESTThe Approximate Solutions of Three-Dimensional Diffusion and Wave Equations within Local Fractional Derivative Operatorhttp://projecteuclid.org/euclid.aaa/1481943742<strong>Hassan Kamil Jassim</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2016, 5 pages.</p><p><strong>Abstract:</strong><br/> We used the local fractional variational iteration transform method (LFVITM) coupled by the local fractional Laplace transform and variational iteration method to solve three-dimensional diffusion and wave equations with local fractional derivative operator. This method has Lagrange multiplier equal to minus one, which makes the calculations more easily. The obtained results show that the presented method is efficient and yields a solution in a closed form. Illustrative examples are included to demonstrate the high accuracy and fast convergence of this new method. </p>projecteuclid.org/euclid.aaa/1481943742_20161216220306Fri, 16 Dec 2016 22:03 ESTCompleteness of Ordered Fields and a Trio of Classical Series Testshttp://projecteuclid.org/euclid.aaa/1481943743<strong>Robert Kantrowitz</strong>, <strong>Michael M. Neumann</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2016, 6 pages.</p><p><strong>Abstract:</strong><br/> This article explores the fate of the infinite series tests of Dirichlet, Dedekind, and Abel in the context of an arbitrary ordered field. It is shown that each of these three tests characterizes the Dedekind completeness of an Archimedean ordered field; specifically, none of the three is valid in any proper subfield of $\mathbb{R}$ . The argument hinges on a contractive-type property for sequences in Archimedean ordered fields that are bounded and strictly increasing. For an arbitrary ordered field, it turns out that each of the tests of Dirichlet and Dedekind is equivalent to the sequential completeness of the field. </p>projecteuclid.org/euclid.aaa/1481943743_20161216220306Fri, 16 Dec 2016 22:03 ESTFréchet Envelopes of Nonlocally Convex Variable Exponent Hörmander Spaceshttp://projecteuclid.org/euclid.aaa/1481943744<strong>Joaquín Motos</strong>, <strong>María Jesús Planells</strong>, <strong>César F. Talavera</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2016, 9 pages.</p><p><strong>Abstract:</strong><br/> We show that the dual ${({B}_{p(·)}^{\mathrm{l}\mathrm{o}\mathrm{c}}(\mathrm{\Omega }))}^{\mathrm{\prime }}$ of the variable exponent Hörmander space ${B}_{p(·)}^{\mathrm{l}\mathrm{o}\mathrm{c}}(\mathrm{\Omega })$ is isomorphic to the Hörmander space ${B}_{\mathrm{\infty }}^{c}(\mathrm{\Omega })$ (when the exponent $p(·)$ satisfies the conditions $\mathrm{0}<{p}^{-}\le {p}^{+}\le \mathrm{1}$ , the Hardy-Littlewood maximal operator $M$ is bounded on ${L}_{p(·)/{p}_{\mathrm{0}}}$ for some $\mathrm{0}<{p}_{\mathrm{0}}<{p}^{-}$ and $\mathrm{\Omega }$ is an open set in ${\mathbb{R}}^{n}$ ) and that the Fréchet envelope of ${B}_{p(·)}^{\mathrm{l}\mathrm{o}\mathrm{c}}(\mathrm{\Omega })$ is the space ${B}_{\mathrm{1}}^{\mathrm{l}\mathrm{o}\mathrm{c}}(\mathrm{\Omega })$ . Our proofs rely heavily on the properties of the Banach envelopes of the ${p}_{\mathrm{0}}$ -Banach local spaces of ${B}_{p(·)}^{\mathrm{l}\mathrm{o}\mathrm{c}}(\mathrm{\Omega })$ and on the inequalities established in the extrapolation theorems in variable Lebesgue spaces of entire analytic functions obtained in a previous article. Other results for $p(·)\equiv p$ , $\mathrm{0}<p<\mathrm{1}$ , are also given (e.g., all quasi-Banach subspace of ${B}_{p}^{\mathrm{l}\mathrm{o}\mathrm{c}}(\mathrm{\Omega })$ is isomorphic to a subspace of ${l}_{p}$ , or ${l}_{\mathrm{\infty }}$ is not isomorphic to a complemented subspace of the Shapiro space ${h}_{{p}^{-}}$ ). Finally, some questions are proposed. </p>projecteuclid.org/euclid.aaa/1481943744_20161216220306Fri, 16 Dec 2016 22:03 ESTIntegrodifferential Inequalities Arising in the Theory of Differential Equationshttp://projecteuclid.org/euclid.aaa/1481943745<strong>Zareen A. Khan</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2016, 6 pages.</p><p><strong>Abstract:</strong><br/> The goal of this paper is to achieve some new results related to integrodifferential inequalities of one independent variable which can be applied as a study of qualitative and quantitative properties of solutions of some nonlinear integral equations. </p>projecteuclid.org/euclid.aaa/1481943745_20161216220306Fri, 16 Dec 2016 22:03 ESTExistence and Boundedness of Solutions for Nonlinear Volterra Difference Equations in Banach Spaceshttp://projecteuclid.org/euclid.aaa/1481943746<strong>Rigoberto Medina</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2016, 6 pages.</p><p><strong>Abstract:</strong><br/> We consider a class of nonlinear discrete-time Volterra equations in Banach spaces. Estimates for the norm of operator-valued functions and the resolvents of quasi-nilpotent operators are used to find sufficient conditions that all solutions of such equations are elements of an appropriate Banach space. These estimates give us explicit boundedness conditions. The boundedness of solutions to Volterra equations with infinite delay is also investigated. </p>projecteuclid.org/euclid.aaa/1481943746_20161216220306Fri, 16 Dec 2016 22:03 ESTA Variational Approach to Perturbed Discrete Anisotropic Equationshttp://projecteuclid.org/euclid.aaa/1481943747<strong>Amjad Salari</strong>, <strong>Giuseppe Caristi</strong>, <strong>David Barilla</strong>, <strong>Alfio Puglisi</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2016, 12 pages.</p><p><strong>Abstract:</strong><br/> We continue the study of discrete anisotropic equations and we will provide new multiplicity results of the solutions for a discrete anisotropic equation. We investigate the existence of infinitely many solutions for a perturbed discrete anisotropic boundary value problem. The approach is based on variational methods and critical point theory. </p>projecteuclid.org/euclid.aaa/1481943747_20161216220306Fri, 16 Dec 2016 22:03 ESTA Simplified Proof of Uncertainty Principle for Quaternion Linear Canonical Transformhttp://projecteuclid.org/euclid.aaa/1455115144<strong>Mawardi Bahri</strong>, <strong>Ryuichi Ashino</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2016, 11 pages.</p><p><strong>Abstract:</strong><br/> We provide a short and simple proof of an uncertainty principle associated with the quaternion linear canonical transform (QLCT) by considering the fundamental relationship between the QLCT and the quaternion Fourier transform (QFT). We show how this relation allows us to derive the inverse transform and Parseval and Plancherel formulas associated with the QLCT. Some other properties of the QLCT are also studied. </p>projecteuclid.org/euclid.aaa/1455115144_20170124220641Tue, 24 Jan 2017 22:06 ESTLocal Hypoellipticity by Lyapunov Functionhttp://projecteuclid.org/euclid.aaa/1455115145<strong>E. R. Aragão-Costa</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2016, 8 pages.</p><p><strong>Abstract:</strong><br/> We treat the local hypoellipticity, in the first degree, for a class of abstract differential operators complexes; the ones are given by the following differential operators: ${L}_{j}=\partial /\partial {t}_{j}+(\partial \varphi /\partial {t}_{j})(t,A)A$ , $j=\mathrm{1,2},\dots ,n$ , where $A:D(A)\subset H\to H$ is a self-adjoint linear operator, positive with $\mathrm{0}\in \rho (A)$ , in a Hilbert space $H$ , and $\varphi =\varphi (t,A)$ is a series of nonnegative powers of ${A}^{-\mathrm{1}}$ with coefficients in ${C}^{\mathrm{\infty }}(\mathrm{\Omega })$ , $\mathrm{\Omega }$ being an open set of ${\mathbb{R}}^{n}$ , for any $n\in \mathbb{N}$ , different from what happens in the work of Hounie (1979) who studies the problem only in the case $n=\mathrm{1}$ . We provide sufficient condition to get the local hypoellipticity for that complex in the elliptic region, using a Lyapunov function and the dynamics properties of solutions of the Cauchy problem $t$ ′ $(s)=-\nabla \mathrm{R}\mathrm{e}\mathrm{}{\varphi }_{\mathrm{0}}(t(s))$ , $s\ge \mathrm{0}$ , $t(\mathrm{0})={t}_{\mathrm{0}}\in \mathrm{\Omega },{\varphi }_{\mathrm{0}}:\mathrm{\Omega }\to \mathbb{C}$ being the first coefficient of $\varphi (t,A)$ . Besides, to get over the problem out of the elliptic region, that is, in the points $t$ ∗ $\in \mathrm{\Omega }$ such that $\nabla \mathrm{R}\mathrm{e}{\varphi }_{\mathrm{0}}(t$ ∗ $)$ = 0, we will use the techniques developed by Bergamasco et al. (1993) for the particular operator $A=\mathrm{1}-\mathrm{\Delta }:{H}^{\mathrm{2}}({\mathbb{R}}^{N})\subset {L}^{\mathrm{2}}({\mathbb{R}}^{N})\to {L}^{\mathrm{2}}({\mathbb{R}}^{N})$ . </p>projecteuclid.org/euclid.aaa/1455115145_20170124220641Tue, 24 Jan 2017 22:06 ESTGeneration and Identification of Ordinary Differential Equations of Maximal Symmetry Algebrahttp://projecteuclid.org/euclid.aaa/1485313541<strong>J. C. Ndogmo</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2016, 9 pages.</p><p><strong>Abstract:</strong><br/> An effective method for generating linear ordinary differential equations of maximal symmetry in their most general form is found, and an explicit expression for the point transformation reducing the equation to its canonical form is obtained. New expressions for the general solution are also found, as well as several identification and other results and a direct proof of the fact that a linear ordinary differential equation is iterative if and only if it is reducible to the canonical form by a point transformation. New classes of solvable equations parameterized by an arbitrary function are also found, together with simple algebraic expressions for the corresponding general solution. </p>projecteuclid.org/euclid.aaa/1485313541_20170124220641Tue, 24 Jan 2017 22:06 ESTA Variation on Uncertainty Principle and Logarithmic Uncertainty Principle
for Continuous Quaternion Wavelet Transformshttp://projecteuclid.org/euclid.aaa/1488423778<strong>Mawardi Bahri</strong>, <strong>Ryuichi Ashino</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 11 pages.</p><p><strong>Abstract:</strong><br/>
The continuous quaternion wavelet transform(CQWT) is a generalization of the classical continuous wavelet transformwithin the
context of quaternion algebra. First of all, we show that the directional quaternion Fourier transform (QFT) uncertainty principle
can be obtained using the component-wise QFT uncertainty principle. Based on this method, the directional QFT uncertainty
principle using representation of polar coordinate form is easily derived. We derive a variation on uncertainty principle related
to the QFT. We state that the CQWT of a quaternion function can be written in terms of the QFT and obtain a variation on
uncertainty principle related to the CQWT. Finally, we apply the extended uncertainty principles and properties of the CQWT to
establish logarithmic uncertainty principles related to generalized transform.
</p>projecteuclid.org/euclid.aaa/1488423778_20170301220315Wed, 01 Mar 2017 22:03 ESTBoundedness Criteria and Norm of Some Multilinear Hilbert-Type Operatorshttp://projecteuclid.org/euclid.aaa/1491962535<strong>Justice S. Bansah</strong>, <strong>Benoît F. Sehba</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 13 pages.</p><p><strong>Abstract:</strong><br/>
We consider two families of multilinear Hilbert-type operators for which we give exact relations between the parameters so that they are bounded. We also find the exact norm of these operators.
</p>projecteuclid.org/euclid.aaa/1491962535_20170411220232Tue, 11 Apr 2017 22:02 EDTModification of Nonlinear Conjugate Gradient Method with Weak Wolfe-Powell Line Searchhttp://projecteuclid.org/euclid.aaa/1491962536<strong>Ahmad Alhawarat</strong>, <strong>Zabidin Salleh</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 6 pages.</p><p><strong>Abstract:</strong><br/>
Conjugate gradient (CG) method is used to find the optimum solution for the large scale unconstrained optimization problems. Based on its simple algorithm, low memory requirement, and the speed of obtaining the solution, this method is widely used in many fields, such as engineering, computer science, and medical science. In this paper, we modified CG method to achieve the global convergence with various line searches. In addition, it passes the sufficient descent condition without any line search. The numerical computations under weak Wolfe-Powell line search shows that the efficiency of the new method is superior to other conventional methods.
</p>projecteuclid.org/euclid.aaa/1491962536_20170411220232Tue, 11 Apr 2017 22:02 EDTSome Notes about the Continuous-in-Time Financial Modelhttp://projecteuclid.org/euclid.aaa/1491962537<strong>Tarik Chakkour</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 11 pages.</p><p><strong>Abstract:</strong><br/>
In this paper, we investigate the properties of operators in the continuous-in-time model which is designed to be used for the finances of public institutions. These operators are involved in the inverse problem of this model. We discuss this inverse problem in Schwartz space that we prove the uniqueness theorem.
</p>projecteuclid.org/euclid.aaa/1491962537_20170411220232Tue, 11 Apr 2017 22:02 EDTOn Approximations by Trigonometric Polynomials of Classes of Functions Defined by Moduli of Smoothnesshttp://projecteuclid.org/euclid.aaa/1491962538<strong>Nimete Sh. Berisha</strong>, <strong>Faton M. Berisha</strong>, <strong>Mikhail K. Potapov</strong>, <strong>Marjan Dema</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 11 pages.</p><p><strong>Abstract:</strong><br/>
In this paper, we give a characterization of Nikol’skiĭ-Besov type classes of functions, given by integral representations of moduli of smoothness, in terms of series over the moduli of smoothness. Also, necessary and sufficient conditions in terms of monotone or lacunary Fourier coefficients for a function to belong to such a class are given. In order to prove our results, we make use of certain recent reverse Copson-type and Leindler-type inequalities.
</p>projecteuclid.org/euclid.aaa/1491962538_20170411220232Tue, 11 Apr 2017 22:02 EDTNew Conditions for the Exponential Stability of Nonlinear Differential Equationshttp://projecteuclid.org/euclid.aaa/1494468086<strong>Rigoberto Medina</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 7 pages.</p><p><strong>Abstract:</strong><br/>
We develop a method for proving local exponential stability of nonlinear nonautonomous differential equations as well as pseudo-linear differential systems. The logarithmic norm technique combined with the “freezing” method is used to study stability of differential systems with slowly varying coefficients and nonlinear perturbations. Testable conditions for local exponential stability of pseudo-linear differential systems are given. Besides, we establish the robustness of the exponential stability in finite-dimensional spaces, in the sense that the exponential stability for a given linear equation persists under sufficiently small perturbations. We illustrate the application of this test to linear approximations of the differential systems under consideration.
</p>projecteuclid.org/euclid.aaa/1494468086_20170510220138Wed, 10 May 2017 22:01 EDTItô’s Formula, the Stochastic Exponential, and Change of Measure on General Time Scaleshttp://projecteuclid.org/euclid.aaa/1494468087<strong>Wenqing Hu</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 13 pages.</p><p><strong>Abstract:</strong><br/>
We provide an Itô formula for stochastic dynamical equation on general time scales. Based on this Itô’s formula we give a closed-form expression for stochastic exponential on general time scales. We then demonstrate Girsanov’s change of measure formula in the case of general time scales. Our result is being applied to a Brownian motion on the quantum time scale ( $q$ -time scale).
</p>projecteuclid.org/euclid.aaa/1494468087_20170510220138Wed, 10 May 2017 22:01 EDTNonnegative Infinite Matrices that Preserve $(p,q)$ -Convexity of Sequenceshttp://projecteuclid.org/euclid.aaa/1497578540<strong>Chikkanna R. Selvaraj</strong>, <strong>Suguna Selvaraj</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 9 pages.</p><p><strong>Abstract:</strong><br/>
This paper deals with matrix transformations that preserve the $(p,q)$ -convexity of sequences. The main result gives the necessary
and sufficient conditions for a nonnegative infinite matrix $A$ to preserve the $(p,q)$ -convexity of sequences. Further, we give examples of such
matrices for different values of $p$ and $q$ .
</p>projecteuclid.org/euclid.aaa/1497578540_20170615220243Thu, 15 Jun 2017 22:02 EDTOn the Boundedness of the Fractional Bergman Operatorshttp://projecteuclid.org/euclid.aaa/1497578541<strong>Benoît F. Sehba</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 3 pages.</p><p><strong>Abstract:</strong><br/>
We give a necessary and sufficient condition for the boundedness of the
Bergman fractional operators.
</p>projecteuclid.org/euclid.aaa/1497578541_20170615220243Thu, 15 Jun 2017 22:02 EDTCorrigendum to “Existence of Solutions for a Coupled System of
Second and Fourth Order Elliptic Equations”http://projecteuclid.org/euclid.aaa/1497578542<strong>Fanglei Wang</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 1 page.</p>projecteuclid.org/euclid.aaa/1497578542_20170615220243Thu, 15 Jun 2017 22:02 EDTOn the Convergence of the Uniform Attractor for the 2D Leray- α
Modelhttp://projecteuclid.org/euclid.aaa/1497578543<strong>Gabriel Deugoué</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 11 pages.</p><p><strong>Abstract:</strong><br/>
We consider a nonautonomous 2D Leray- $\alpha $ model of fluid turbulence. We prove the existence of the
uniform attractor ${\mathcal{A}}^{\alpha }$ . We also study the convergence of ${\mathcal{A}}^{\alpha }$ as $\alpha $ goes to zero. More precisely, we prove that the uniform
attractor ${\mathcal{A}}^{\alpha }$ converges to the uniform attractor of the 2D Navier-Stokes
system as $\alpha $ tends to zero.
</p>projecteuclid.org/euclid.aaa/1497578543_20170615220243Thu, 15 Jun 2017 22:02 EDTApproximation of Durrmeyer Type Operators Depending on Certain
Parametershttp://projecteuclid.org/euclid.aaa/1497578544<strong>Neha Malik</strong>, <strong>Serkan Araci</strong>, <strong>Man Singh Beniwal</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 9 pages.</p><p><strong>Abstract:</strong><br/>
Motivated by a number of recent investigations, we consider a new
analogue of Bernstein-Durrmeyer operators based on certain variants.
We derive some approximation properties of these operators. We also
compute local approximation and Voronovskaja type asymptotic formula.
We illustrate the convergence of aforementioned operators by making
use of the software MATLAB which we stated in the paper.
</p>projecteuclid.org/euclid.aaa/1497578544_20170615220243Thu, 15 Jun 2017 22:02 EDTA New Class of Contraction in $b$ -Metric Spaces and Applicationshttp://projecteuclid.org/euclid.aaa/1500429779<strong>Preeti Kaushik</strong>, <strong>Sanjay Kumar</strong>, <strong>Kenan Tas</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 10 pages.</p><p><strong>Abstract:</strong><br/>
A novel class of $\alpha $ - $\beta $ -contraction for a pair of mappings is introduced in the setting of $b$ -metric spaces. Existence and uniqueness of coincidence and common fixed
points for such kind of mappings are investigated. Results are supported with
relevant examples. At the end, results are applied to find the solution of an
integral equation.
</p>projecteuclid.org/euclid.aaa/1500429779_20170718220321Tue, 18 Jul 2017 22:03 EDTWeak and Strong Solutions for a Strongly Damped Quasilinear Membrane
Equationhttp://projecteuclid.org/euclid.aaa/1500429780<strong>Jin-soo Hwang</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 9 pages.</p><p><strong>Abstract:</strong><br/>
We consider a strongly damped quasilinear membrane equation with Dirichlet
boundary condition. The goal is to prove the well-posedness of the equation in
weak and strong senses. By setting suitable function spaces and making use of
the properties of the quasilinear term in the equation, we have proved the
fundamental results on existence, uniqueness, and continuous dependence on data
including bilinear term of weak and strong solutions.
</p>projecteuclid.org/euclid.aaa/1500429780_20170718220321Tue, 18 Jul 2017 22:03 EDTGeneralized Hölder’s and Minkowski’s Inequalities for
Jackson’s $q$ -Integral and Some Applications to the Incomplete $q$ -Gamma Functionhttp://projecteuclid.org/euclid.aaa/1502762543<strong>Kwara Nantomah</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 6 pages.</p><p><strong>Abstract:</strong><br/>
We establish some generalized Hölder’s and Minkowski’s
inequalities for Jackson’s $q$ -integral. As applications, we derive some inequalities involving the
incomplete $q$ -Gamma function.
</p>projecteuclid.org/euclid.aaa/1502762543_20170814220252Mon, 14 Aug 2017 22:02 EDTThe Approximation Szász-Chlodowsky Type Operators Involving Gould-Hopper
Type Polynomialshttp://projecteuclid.org/euclid.aaa/1502762544<strong>Behar Baxhaku</strong>, <strong>Artan Berisha</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 8 pages.</p><p><strong>Abstract:</strong><br/>
We introduce the Szász and Chlodowsky operators based on Gould-Hopper
polynomials and study the statistical convergence of these operators in a
weighted space of functions on a positive semiaxis. Further, a Voronovskaja type
result is obtained for the operators containing Gould-Hopper polynomials.
Finally, some graphical examples for the convergence of this type of operator
are given.
</p>projecteuclid.org/euclid.aaa/1502762544_20170814220252Mon, 14 Aug 2017 22:02 EDTOn Weighted Montgomery Identity for $k$ Points and Its Associates on Time Scaleshttp://projecteuclid.org/euclid.aaa/1502762545<strong>Eze R. Nwaeze</strong>, <strong>Ana M. Tameru</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 7 pages.</p><p><strong>Abstract:</strong><br/>
The purpose of this paper is to establish a weighted Montgomery identity for
$k$ points and then use this identity to prove a new weighted Ostrowski type
inequality. Our results boil down to the results of Liu and Ngô if we take
the weight function to be the identity map. In addition, we also generalize an
inequality of Ostrowski-Grüss type on time scales for $k$ points. For $k=\mathrm{2},$ we recapture a result of Tuna and Daghan. Finally, we apply our results
to the continuous, discrete, and quantum calculus to obtain more results in this
direction.
</p>projecteuclid.org/euclid.aaa/1502762545_20170814220252Mon, 14 Aug 2017 22:02 EDTBifurcation and Global Dynamics of a Leslie-Gower Type Competitive System of Rational Difference Equations with Quadratic Termshttps://projecteuclid.org/euclid.aaa/1505786568<strong>V. Hadžiabdić</strong>, <strong>M. R. S. Kulenović</strong>, <strong>E. Pilav</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 19 pages.</p><p><strong>Abstract:</strong><br/>
We investigate global dynamics of the following systems of difference equations ${x}_{n+\mathrm{1}}={x}_{n}/({A}_{\mathrm{1}}+{B}_{\mathrm{1}}{x}_{n}+{C}_{\mathrm{1}}{y}_{n})$ , ${y}_{n+\mathrm{1}}={y}_{n}^{\mathrm{2}}/({A}_{\mathrm{2}}+{B}_{\mathrm{2}}{x}_{n}+{C}_{\mathrm{2}}{y}_{n}^{\mathrm{2}})$ , $n=\mathrm{0,1},\dots $ , where the parameters ${A}_{\mathrm{1}}$ , ${A}_{\mathrm{2}}$ , ${B}_{\mathrm{1}}$ , ${B}_{\mathrm{2}}$ , ${C}_{\mathrm{1}}$ , and ${C}_{\mathrm{2}}$ are positive numbers and the initial conditions ${x}_{\mathrm{0}}$ and ${y}_{\mathrm{0}}$ are arbitrary nonnegative numbers. This system is a version of the Leslie-Gower competition model for two species. We show that this system has rich dynamics which depends on the part of parametric space.
</p>projecteuclid.org/euclid.aaa/1505786568_20170918220316Mon, 18 Sep 2017 22:03 EDTA Degree Theory for Compact Perturbations of Monotone Type Operators and
Application to Nonlinear Parabolic Problemhttps://projecteuclid.org/euclid.aaa/1507687470<strong>Teffera M. Asfaw</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 13 pages.</p><p><strong>Abstract:</strong><br/>
Let $X$ be a real locally uniformly convex reflexive Banach space with
locally uniformly convex dual space ${X}^{*}$ . Let $T:X\supseteq D(T)\to {\mathrm{2}}^{{X}^{*}}$ be maximal monotone, $S:X\to {\mathrm{2}}^{{X}^{*}}$ be bounded and of type $({S}_{+}),$ and $C:D(C)\to {X}^{*}$ be compact with $D(T)\subseteq D(C)$ such that $C$ lies in ${\mathrm{\Gamma }}_{\sigma }^{\tau }$ (i.e., there exist $\sigma \ge \mathrm{0}$ and $\tau \ge \mathrm{0}$ such that $‖Cx‖\le \tau ‖x‖+\sigma $ for all $x\in D(C)$ ). A new topological degree theory is developed for operators
of the type $T+S+C$ . The theory is essential because no degree theory and/or
existence result is available to address solvability of operator
inclusions involving operators of the type $T+S+C$ , where $C$ is not defined everywhere. Consequently, new existence
theorems are provided. The existence theorem due to Asfaw and
Kartsatos is improved. The theory is applied to prove existence of
weak solution (s) for a nonlinear parabolic problem in appropriate
Sobolev spaces.
</p>projecteuclid.org/euclid.aaa/1507687470_20171010220505Tue, 10 Oct 2017 22:05 EDTOn Singular Solutions to PDEs with Turning Point Involving a Quadratic
Nonlinearityhttps://projecteuclid.org/euclid.aaa/1507687471<strong>Stéphane Malek</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 32 pages.</p><p><strong>Abstract:</strong><br/>
We study a singularly perturbed PDE with quadratic nonlinearity depending
on a complex perturbation parameter $\mathrm{ϵ}$ . The problem involves an irregular singularity in time, as in
a recent work of the author and A. Lastra, but possesses also, as a
new feature, a turning point at the origin in $\mathbb{C}$ . We construct a family of sectorial meromorphic solutions
obtained as a small perturbation in $\mathrm{ϵ}$ of a slow curve of the equation in some time scale. We show
that the nonsingular parts of these solutions share common formal
power series (that generally diverge) in $\mathrm{ϵ}$ as Gevrey asymptotic expansion of some order depending on data
arising both from the turning point and from the irregular singular
point of the main problem.
</p>projecteuclid.org/euclid.aaa/1507687471_20171010220505Tue, 10 Oct 2017 22:05 EDTThree Different Methods for New Soliton Solutions of the Generalized NLS Equationhttps://projecteuclid.org/euclid.aaa/1510801630<strong>Anwar Ja’afar Mohamad Jawad</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 8 pages.</p><p><strong>Abstract:</strong><br/>
Three different methods are applied to construct new types of solutions of nonlinear evolution equations. First, the Csch method is used to carry out the solutions; then the Extended Tanh-Coth method and the modified simple equation method are used to obtain the soliton solutions. The effectiveness of these methods is demonstrated by applications to the RKL model, the generalized derivative NLS equation. The solitary wave solutions and trigonometric function solutions are obtained. The obtained solutions are very useful in the nonlinear pulse propagation through optical fibers.
</p>projecteuclid.org/euclid.aaa/1510801630_20171115220745Wed, 15 Nov 2017 22:07 ESTThe Jump Size Distribution of the Commodity Spot Price and Its Effect on Futures and Option Priceshttps://projecteuclid.org/euclid.aaa/1510801634<strong>L. Gómez-Valle</strong>, <strong>Z. Habibilashkary</strong>, <strong>J. Martínez-Rodríguez</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 10 pages.</p><p><strong>Abstract:</strong><br/>
In this paper, we analyze the role of the jump size distribution in the US natural gas prices when valuing natural gas futures traded at New York Mercantile Exchange (NYMEX) and we observe that a jump-diffusion model always provides lower errors than a diffusion model. Moreover, we also show that although the Normal distribution offers lower errors for short maturities, the Exponential distribution is quite accurate for long maturities. We also price natural gas options and we see that, in general, the model with the Normal jump size distribution underprices these options with respect to the Exponential distribution. Finally, we obtain the futures risk premia in both cases and we observe that for long maturities the term structure of the risk premia is negative. Moreover, the Exponential distribution provides the highest premia in absolute value.
</p>projecteuclid.org/euclid.aaa/1510801634_20171115220745Wed, 15 Nov 2017 22:07 ESTApplications of the $g$ -Drazin Inverse to the Heat Equation and a Delay Differential Equationhttps://projecteuclid.org/euclid.aaa/1513220438<strong>Alrazi Abdeljabbar</strong>, <strong>Trung Dinh Tran</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 4 pages.</p><p><strong>Abstract:</strong><br/>
We consider applications of the $g$ -Drazin inverse to some classes of abstract Cauchy problems, namely, the heat equation with operator coefficient and delay differential equations in Banach space.
</p>projecteuclid.org/euclid.aaa/1513220438_20171213220130Wed, 13 Dec 2017 22:01 ESTCorrigendum to “Noncoercive Perturbed Densely Defined Operators and Application to Parabolic Problems”https://projecteuclid.org/euclid.aaa/1513220443<strong>Teffera M. Asfaw</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 1 page.</p>projecteuclid.org/euclid.aaa/1513220443_20171213220130Wed, 13 Dec 2017 22:01 ESTImproving Fourier Partial Sum Approximation for Discontinuous Functions Using a Weight Functionhttps://projecteuclid.org/euclid.aaa/1513220444<strong>Beong In Yun</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 7 pages.</p><p><strong>Abstract:</strong><br/>
We introduce a generalized sigmoidal transformation ${w}_{m}(r;x)$ on a given interval $[a,b]$ with a threshold at $x=r\in (a,b)$ . Using ${w}_{m}(r;x)$ , we develop a weighted averaging method in order to improve Fourier partial sum approximation for a function having a jump-discontinuity. The method is based on the decomposition of the target function into the left-hand and the right-hand part extensions. The resultant approximate function is composed of the Fourier partial sums of each part extension. The pointwise convergence of the presented method and its availability for resolving Gibbs phenomenon are proved. The efficiency of the method is shown by some numerical examples.
</p>projecteuclid.org/euclid.aaa/1513220444_20171213220130Wed, 13 Dec 2017 22:01 ESTOn the Output Controllability of Positive Discrete Linear Delay Systemshttps://projecteuclid.org/euclid.aaa/1513220445<strong>Mouhcine Naim</strong>, <strong>Fouad Lahmidi</strong>, <strong>Abdelwahed Namir</strong>, <strong>Mostafa Rachik</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 12 pages.</p><p><strong>Abstract:</strong><br/>
Necessary and sufficient conditions for output reachability and null output controllability of positive linear discrete systems with delays in state, input, and output are established. It is also shown that output reachability and null output controllability together imply output controllability.
</p>projecteuclid.org/euclid.aaa/1513220445_20171213220130Wed, 13 Dec 2017 22:01 ESTCorrigendum to “A Three-Point Boundary Value Problem with an Integral Condition for a Third-Order Partial Differential Equation”https://projecteuclid.org/euclid.aaa/1513220446<strong>C. Latrous</strong>, <strong>A. Memou</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 1 page.</p>projecteuclid.org/euclid.aaa/1513220446_20171213220130Wed, 13 Dec 2017 22:01 ESTApproximation Properties of $q$ -Bernoulli Polynomialshttps://projecteuclid.org/euclid.aaa/1515466879<strong>M. Momenzadeh</strong>, <strong>I. Y. Kakangi</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 6 pages.</p><p><strong>Abstract:</strong><br/>
We study the $q$ -analogue of Euler-Maclaurin formula and by introducing a new $q$ -operator we drive to this form. Moreover, approximation properties of $q$ -Bernoulli polynomials are discussed. We estimate the suitable functions as a combination of truncated series of $q$ -Bernoulli polynomials and the error is calculated. This paper can be helpful in two different branches: first we solve the differential equations by estimating functions and second we may apply these techniques for operator theory.
</p>projecteuclid.org/euclid.aaa/1515466879_20180108220206Mon, 08 Jan 2018 22:02 ESTFinite-Time Stability and Controller Design of Continuous-Time Polynomial Fuzzy Systemshttps://projecteuclid.org/euclid.aaa/1515466880<strong>Xiaoxing Chen</strong>, <strong>Manfeng Hu</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 12 pages.</p><p><strong>Abstract:</strong><br/>
Finite-time stability and stabilization problem is first investigated for continuous-time polynomial fuzzy systems. The concept of finite-time stability and stabilization is given for polynomial fuzzy systems based on the idea of classical references. A sum-of-squares- (SOS-) based approach is used to obtain the finite-time stability and stabilization conditions, which include some classical results as special cases. The proposed conditions can be solved with the help of powerful Matlab toolbox SOSTOOLS and a semidefinite-program (SDP) solver. Finally, two numerical examples and one practical example are employed to illustrate the validity and effectiveness of the provided conditions.
</p>projecteuclid.org/euclid.aaa/1515466880_20180108220206Mon, 08 Jan 2018 22:02 ESTContractibility of Fixed Point Sets of Mean-Type Mappingshttps://projecteuclid.org/euclid.aaa/1515466882<strong>S. Iampiboonvatana</strong>, <strong>P. Chaoha</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 7 pages.</p><p><strong>Abstract:</strong><br/>
We establish a convergence theorem and explore fixed point sets of certain continuous quasi-nonexpansive mean-type mappings in general normed linear spaces. We not only extend previous works by Matkowski to general normed linear spaces, but also obtain a new result on the structure of fixed point sets of quasi-nonexpansive mappings in a nonstrictly convex setting.
</p>projecteuclid.org/euclid.aaa/1515466882_20180108220206Mon, 08 Jan 2018 22:02 ESTNecessary and Sufficient Conditions for Set-Valued Maps with Set Optimizationhttps://projecteuclid.org/euclid.aaa/1518577260<strong>Abdessamad Oussarhan</strong>, <strong>Ikram Daidai</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 6 pages.</p><p><strong>Abstract:</strong><br/>
Optimality conditions are studied for set-valued maps with set optimization. Necessary conditions are given in terms of $S$ -derivative and contingent derivative. Sufficient conditions for the existence of solutions are shown for set-valued maps under generalized quasiconvexity assumptions.
</p>projecteuclid.org/euclid.aaa/1518577260_20180213220118Tue, 13 Feb 2018 22:01 ESTSoliton Solutions of the Coupled Schrödinger-Boussinesq Equations for Kerr Law Nonlinearityhttps://projecteuclid.org/euclid.aaa/1518577262<strong>Anwar Ja’afar Mohamad Jawad</strong>, <strong>Mahmood Jawad Abu-AlShaeer</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 8 pages.</p><p><strong>Abstract:</strong><br/>
In this paper, the coupled Schrödinger-Boussinesq equations (SBE) will be solved by the sech, tanh, csch, and the modified simplest equation method (MSEM). We obtain exact solutions of the nonlinear for bright, dark, and singular 1-soliton solution. Kerr law nonlinearity media are studied. Results have proven that modified simple equation method does not produce the soliton solution in general case. Solutions may find practical applications and will be important for the conservation laws for dispersive optical solitons.
</p>projecteuclid.org/euclid.aaa/1518577262_20180213220118Tue, 13 Feb 2018 22:01 ESTGeneralized Asymptotically Almost Periodic and Generalized Asymptotically Almost Automorphic Solutions of Abstract Multiterm Fractional Differential Inclusionshttps://projecteuclid.org/euclid.aaa/1518577263<strong>G. M. N’Guérékata</strong>, <strong>Marko Kostić</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 17 pages.</p><p><strong>Abstract:</strong><br/>
The main aim of this paper is to investigate generalized asymptotical almost periodicity and generalized asymptotical almost automorphy of solutions to a class of abstract (semilinear) multiterm fractional differential inclusions with Caputo derivatives. We illustrate our abstract results with several examples and possible applications.
</p>projecteuclid.org/euclid.aaa/1518577263_20180213220118Tue, 13 Feb 2018 22:01 ESTMultiobjective Optimization, Scalarization, and Maximal Elements of Preordershttps://projecteuclid.org/euclid.aaa/1518577264<strong>Paolo Bevilacqua</strong>, <strong>Gianni Bosi</strong>, <strong>Magalì Zuanon</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 6 pages.</p><p><strong>Abstract:</strong><br/>
We characterize the existence of (weak) Pareto optimal solutions to the classical multiobjective optimization problem by referring to the naturally associated preorders and their finite (Richter-Peleg) multiutility representation. The case of a compact design space is appropriately considered by using results concerning the existence of maximal elements of preorders. The possibility of reformulating the multiobjective optimization problem for determining the weak Pareto optimal solutions by means of a scalarization procedure is finally characterized.
</p>projecteuclid.org/euclid.aaa/1518577264_20180213220118Tue, 13 Feb 2018 22:01 ESTTwo Sufficient Conditions for Convex Ordering on Risk Aggregationhttps://projecteuclid.org/euclid.aaa/1521252060<strong>Dan Zhu</strong>, <strong>Chuancun Yin</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 5 pages.</p><p><strong>Abstract:</strong><br/>
We define new stochastic orders in higher dimensions called weak correlation orders. It is shown that weak correlation orders imply stop-loss order of sums of multivariate dependent risks with the same marginals. Moreover, some properties and relations of stochastic orders are discussed.
</p>projecteuclid.org/euclid.aaa/1521252060_20180316220113Fri, 16 Mar 2018 22:01 EDTStability for Linear Volterra Difference Equations in Banach Spaceshttps://projecteuclid.org/euclid.aaa/1523498503<strong>Rigoberto Medina</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 6 pages.</p><p><strong>Abstract:</strong><br/>
This paper is devoted to studying the existence and stability of implicit Volterra difference equations in Banach spaces. The proofs of our results are carried out by using an appropriate extension of the freezing method to Volterra difference equations in Banach spaces. Besides, sharp explicit stability conditions are derived.
</p>projecteuclid.org/euclid.aaa/1523498503_20180411220152Wed, 11 Apr 2018 22:01 EDTTime Scale Inequalities of the Ostrowski Type for Functions Differentiable on the Coordinateshttps://projecteuclid.org/euclid.aaa/1523498504<strong>Eze R. Nwaeze</strong>, <strong>Seth Kermausuor</strong>, <strong>Ana M. Tameru</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 10 pages.</p><p><strong>Abstract:</strong><br/>
In 2016, some inequalities of the Ostrowski type for functions (of two variables) differentiable on the coordinates were established. In this paper, we extend these results to an arbitrary time scale by means of a parameter $\lambda \in [\mathrm{0,1}]$ . The aforementioned results are regained for the case when the time scale $\mathbb{T}=\mathbb{R}$ . Besides extension, our results are employed to the continuous and discrete calculus to get some new inequalities in this direction.
</p>projecteuclid.org/euclid.aaa/1523498504_20180411220152Wed, 11 Apr 2018 22:01 EDT