In this paper we introduce and study a new subclass of meromorphically uniformly convex functions with positive coefficients defined by a differential operator and obtain coefficient estimates, growth and distortion theorem, radius of convexity,integral transforms, convex linear combinations, convolution properties and $\delta$-neighborhoods for the class $\Sigma_{p}(\alpha , \beta )$.

In this paper, we establish the Hyers-Ulam stability of quintic functional equation in F-spaces by using direct method.

In this study, two bi-univalent function subclasses are defined. The functions are defined in the open unit disc $U$. The main purpose is to determine some estimations on the initial Tayler-Maclaurin coefficients for functions belong to these subclasses. Finally, some earlier results are pointed out and improved.

In this paper we introduce homological and homotopical Poincaré polynomials $P_f(t)$ and $P^{\pi}_f(t)$ of a continuous map $f:X \to Y$ such that if $f$ is a constant map, or more generally, if $Y$ is contractible, then these Poincaré polynomials are respectively equal to the usual homological and homotopical Poincaré polynomials $P_X(t)$ and $P^{\pi}_X(t)$ of the source space $X$. Our relative Hilali conjecture $P^{\pi}_f(1) \leqq P_f(1)$ is a map version of the the well-known Hilali conjecture $P^{\pi}_X(1) \leqq P_X(1)$ of a rationally elliptic space X. In this paper we show that under the condition that $H_i(f;\mathbb Q):H_i(X;\mathbb Q) \to H_i(Y;\mathbb Q)$ is not injective for some $i>0$, the relative Hilali conjecture of product of maps holds, namely, there exists a positive integer $n_0$ such that for $\forall n \geqq n_0$ the strict inequality $P^{\pi}_{f^n}(1) \leq P_{f^n}(1)$ holds. In the final section we pose a question whether a "Hilali"-type inequality $HP^{\pi}_X(r_X) \leqq P_X(r_X)$ holds for a rationally hyperbolic space $X$, provided the the homotopical Hilbert-Poincaré series $HP^{\pi}_X(r_X)$ converges at the radius $r_X$ of convergence.

In this paper, we investigate the following system of difference equations \begin{equation*} x_{n+1}=\frac{\alpha _{n}}{1+y_{n}x_{n-1}},\ y_{n+1}=\frac{\beta _{n}} {1+x_{n}y_{n-1}}, n\in \mathbb{N}_{0}, \end{equation*} where the sequences $\left( \alpha _{n}\right) _{n\in \mathbb{N}_{0}}$, $\left( \beta_{n}\right) _{n\in \mathbb{N}_{0}}$ are positive, real and periodic with period two and the initial values $x_{-1}$, $x_{0}$, $y_{-1}$, $y_{0}$ are non-negative real numbers. We show that every positive solution of the system is bounded and examine their global behaviors. In addition, we give closed forms of the general solutions of the system by using the change of variables. Finally, we present a numerical example to support our results.

In this paper, we have defined hyperbolic type of some iteration methods. The new iteration has been investigated convergence for mappings satisfying certain condition in hyperbolic spaces. It has been proved that this iteration is equivalent in terms of convergence with another iteration method in the same spaces. The rate of convergence of these two iteration methods have been compared. We have investigated data dependence result using hyperbolic type iteration. Finally, we have given numerical examples about rate of convergence and data dependence.

In this paper, we prove the existence of non-critically injective polynomials whose set of zeros form unique range sets that answers one of the most awaited and fundamental questions of uniqueness theory of entire and meromorphic functions. We also show that there exist some unique range sets and their generating polynomials which can not be characterized by any of the existing generalized results of unique range sets but as an application of our main theorems the same can be characterized. Moreover, as an application of our main results we prove that the cardinality of a unique range set does not always depend upon the number of distinct critical points of its generating polynomial.

The recursive computation of the entries of integer powers of a companion matrix are extended to the general case of an infinite-type matrix and the possibility to compute matrix functions of a companion matrix by using the Dunford-Taylor integral is shown.

In this work, we consider a logarithmic Petrovsky equation with strong damping with initial and boundary conditions in a bounded domain. Under suitable conditions, we prove decay of solutions. Also, we establish the blow up at infinite time of solutions.

In this paper a new generalization of $B^*$-continuity has been defined, to be called as $B^*$-clopen continuity and many of its properties have been studied including the convergence behaviour of sequences of such functions. Also a new type of oscillation function, called cl-oscillation has been defined, which characterizes the $B^*$-clopen continuity.

In this article, firstly, based on Taylor series expansion and truncation error correction technology, combined with the fourth-order Padé schemes of the first-order derivatives, a new fourth-order compact difference (CD) scheme is constructed to solve the two-dimensional (2D) linear elliptic equation a mixed derivative. In this new scheme, unknown function and its first-order derivatives are regarded as the unknown variables in calculation. Then, the method is extended to solve the 2D parabolic equation with a mixed derivative. To match the spatial fourth-order accuracy, The backward differentiation formula (BDF) is employed to gain the fourth-order accuracy for the temporal discretization. Truncation error is analyzed to display that the present scheme is fourth-order accuracy in space. In order to solve the resulting large-scale linear equations, a multigrid method is employed to accelerate the convergence speed of the conventional relaxation methods. Finally, numerical results indicate that the present schemes obtain fourth-order convergence and are more accurate than those in the literature.

In this paper, we introduce the generalized Pentanacci quaternions and we present Binet's formulas, generating functions and the summation formulas for these quaternions and as special case for Pentanacci and Pentanacci-Lucas quaternions. Furthermore, we present matrices related to generalized Pentanacci quaternions.

In this paper, we present an extension of Kantorovich inequality for two operators on a Hilbert space. Also, the multiple version and a related inequality for positive linear maps are obtained. Moreover, we introduce the concept of Specht's ratio and improve some inequalities related to Specht's ratio.

In this paper we investigate the existence of solutions for infinite systems of regular fractional Sturm-Liouville problems by an application of Meir-Keeler fixed point theorem in the tempered sequence spaces. We provide examples to check validity of our obtained results.

In this paper, a lopsided modified Euler-extrapolated Hermitian and skew-Hermitian splitting (LME-HS) iteration method is introduced for solving the complex symmetric linear systems. Under a loose restriction on parameter $\theta$, we demonstrate that LME-HS iteration method is convergent. Moreover, we present the optimal parameter ${\theta}^{*}$ of the LME-HS method and discuss the spectral properties of corresponding preconditioned matrix. Finally, the numerical experiments are used to verify the effectiveness of the proposed method.