Diestelkamp, Hartke and Kenney recently studied local permutation polynomials over finite field $F_s$ and proved that $2s-4$ is the sharp bound of their degrees when $s \gt 3$. In this paper, we focus on local permutation polynomials over residue class rings. We prove two specific formulas computing the number and the sharp bound of degrees of local permutation polynomials modulo $p^n$ respectively.

We obtain some results on common fixed points from the set of best simultaneous approximations for a map $T$ which is asymptotically $(f,g)$-nonexpansive where $(T,f)$ and $(T,g)$ are not necessarily commuting pairs. Our results extend and generalize recent results of Chen and Li [1], Jungck and Sessa [8], Sahab et al. [13], Sahney and Singh [14], Singh [15,16] and Vijayaraju [17] and many others.

In this paper we consider the convolution properties of the classes of k-uniformly convex and k-starlike functions which have been introduced in [4], [6]. We investigate the problem of stability of integral convolution on certain pairs of such classes and we give the upper and lower bounds of their radius of stability. In the present paper we improve some of the results obtained in [1].

Let $G$ be a simple undirected graph. Denote by $\mbox{ mi}(G)$ (respectively, $\mbox{xi}(G)$) the number of maximal (respectively, maximum) independent sets in $G$. In this paper we determine the second largest value of $\mbox{mi}(G)$ for graphs with at most $k$ cycles. Extremal graphs achieving these values are also determined.

We develop a theory of simultaneous metric projection in a normed linear space $X$ and present various characterizations of simultaneous metric projection onto closed convex sets in terms of the elements of $X^{\ast}$. Also, we characterize the elements of simultaneous metric projection onto closed convex sets in terms of extreme points of the closed unit ball $B_{X^{\ast}}.$ Finally, as an application, we give various characterizations of simultaneous metric projection onto subspaces of the Banach space $C(Q,Y).$

In this note we derive a formula for the derivative of the CR Yamabe constant $\mathcal{Y}(J_{(t)}),$ where $J_{(t)}$ is a solution of the Cartan flow on a closed CR $3$-manifold. We also give some simple applications.

Let $A=A_{0}\oplus A_{1}$ be a noncommutative prime superalgebra over a commutative associative ring $F$ with $\frac{1}{2}\in F$. Let $Z_{s}(A)$ be the supercenter of $A$. If an $Z_{2}$-preserving automorphism $\varphi: A\rightarrow A$ satisfies $[\varphi(x),x]_{s}\in Z_{s}(A)$ for all $x\in A$, then $\varphi=1$, where $1$ denotes the identity map of $A$. Moreover, if $A_{1}\neq 0$, then $A$ is a central order in a quaternion algebra. This gives a version of Mayne's theorem for superalgebras.

In this paper we investigate modules with the property $C^{*}$ : namely, $M$ has $C^{*}$ if every submodule $N$ of $M$ contains a direct summand $K$ of $M$ such that $N/K$ is cosingular. We prove that every right $R$-module $M$ satisfies $C^{*}$ if and only if every right $R$-module is the direct sum of an injective module and a cosingular module.

We extend the notions of reciprocal continuity and $C_q$-commutativity to nonself setting besides observing equivalence between compatibility and $\phi$ -compatibility, and utilize the same to obtain some results on coincidence and common fixed points for two pairs of nonself mappings in metrically convex metric spaces. As an application of our main result, we also prove a common fixed point theorem in Banach spaces besides furnishing several illustrative examples.

We investigate an American exchange option (AEO) pricing problem. Under the perfect market assumption, an AEO pricing problem can be modeled as a free boundary problem (FBP). The FBP is converted into an integral equation by using the Green’s function. When the expiration date tends to infinity, we obtain a time-invariant constant of the exercise boundary. Moreover, we provide a pricing formula for valuating the early exercise premium of the perpetual AEO.

We provide a few sufficient conditions for a normalized analytic function in the unit disk to be a Bazileviˇc function of prescribed type.

The purpose of this paper is to suggest and analyze a new iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a commutative family of nonexpansive mappings in a Hilbert space. Then we prove a strong convergence theorem which is connected with the results of Takahashi and Takahashi [13] and Yao and Noor [147]. Using this result, we obtain two corollaries which improve and extend their results.

In this paper, we introduce and study some new systems of generalized vector quasi-variational inclusion problems involving condensing mappings in locally $FC$-uniform spaces. These systems contain many known systems of generalized vector quasi-variational inclusion problems, systems of generalized vector quasi-equilibrium problems and systems of vector quasi-optimization problems as special cases. By applying an existence theorem of maximal elements of a family of set-valued mappings involving condensing mapping due to author, we prove some new existence theorems of solutions for the systems of generalized quasi-variational inclusion problems. As applications, some existence results of solutions of the mathematical programs with systems of generalized vector quasi-variational inclusion constraints are established in noncompact locally $FC$-uniform spaces.

In this paper, we propose some parallel and cyclic algorithms based on the extragradient method (nonextragradient method) for finding a common element of the set of solutions of a generalized mixed equilibrium problem, the set of fixed points of a finite family of strict pseudo-contractions and the set of the variational inequality for a monotone, Lipschitz continuous mapping (an inverse strongly monotone mapping). We obtain some weak and strong convergence theorems for the sequences generated by these processes in Hilbert spaces. The results in this paper generalize, improve and unify some well-known results in the literature.

A generalized Bochner-Martinelli formula for the push-forward of a Lipschitz function over a weak Stokes domain is proved. By means of integral products, the $\bar \partial$-Euler and the $\bar \partial$-Neumann vector fields, local and global characterizations of the holomorphicity of functions on a Riemann domain are given. As further applications characterizations of isogeneity and Liouville properties for the push-forward of semi-harmonic functions on an analytic covering space are obtained.

Let $\mu$ be a nonnegative Radon measure satisfying the growth condition that $\mu(B(x,\,r))\leq Cr^{n}$ for any $x\in {\Bbb R}^d$ and $r/gt 0$ and some fixed positive constants $C$ and $n$ with with $0 \lt n\leq d$. Let $H^{1,\,\infty}_{{\rm atb}}(\mu)$ be the Hardy space associated with $\mu$ which was introduced by Tolsa. In this paper, a new interpolation theorems related to $H^{1,\,\infty}_{{\rm atb}}(\mu)$ is established and the interpolation theorem of Tolsa is improved.

The theory of the last multipliers as solutions of the Liouville’s transport equation, previously developed for vector fields, is extended here to general multivectors. Characterizations in terms of Witten and Marsden differentials are reobtained as well as the algebraic structure of the set of multivectors with a common last multiplier, namely Gerstenhaber algebra. Applications to Poisson bivectors are presented by obtaining that last multipliers count for ”how far away” is a Poisson structure from being exact with respect to a given volume form. The notion of exact Poisson cohomology for an unimodular Poisson structure on IRn is introduced.