关于非方常数问题的一个反例

通过一个反例,证明了非方常数为2~(1/2)的相关猜想.     

强预不变凸函数的充要条件

本文讨论了强预不变凸函数与预不变凸函数、严格预不变凸函数及半严格预不变凸函数之间的关系,得到它的三个充要条件：(i)在一定条件下,f是强预不变凸函数的充分必要条件是f是预不变凸函数且f满足中间点强预不变凸性；(ii)在一定条件下,f是强预不变凸函数的充分必要条件是f是严格预不变凸函数且f满足中间点强预不变凸性；(iii)在一定条件下,f是强预不变凸函数的充分必要条件是f是半严格预不变凸函数且f满足中间点强预不变凸性．     

关于全纯映照模的Schwarz引理一点注记

记DC为单位圆盘,B~k C~k为开欧氏单位球,Ω是C~k(或C)中的域.记H_n(D,Ω)为满足一定条件的全纯映照族(或函数族)的全体.作者证明了若,∈Hn(D,D),则|f′(z)|≤(n|z|~(n-1))/(1-|z|~(2n))(1-|f|(z|~2),z∈DD同时,对Hn(D,B~k)中映照的模也得到类似的结果.该结论推广了Pavlovic的相应结果.     

On some Fermat rules for set-valued optimization problems

The aim of this article is to obtain necessary optimality conditions for Pareto minima in set-valued optimization problems. We employ a new method to derive generalized Fermat rules for set-valued optimization. This method is based on openness results for multifunctions and allows recovery of a large number of results and, at the same time, getting several new ones.     

Extended radial epiderivatives of non-convex vector-valued maps and parametric quasiconvex programming

In this paper, we consider extended vector-valued mappings defined on a normed linear space. Based on the recent semicontinuous regularizations related to hypographical and/or epigraphical profile mappings of the considered function introduced, we define semicontinuous radial epiderivatives. We, then, demonstrate that the properties of these epiderivatives amount to properties of hypographical and/or epigraphical profile mappings of the corresponding difference quotient of the underlying function, which simplify fairly well the proofs in the radial epiderivative formulaes. In particular, we stress the impact of semicontinuity, hence, we characterize with new arguments the radial epiderivatives in terms of the suprema and/or infima of the interiorly radial cone of the hypograph and/or epigraph of the considered function. Finally, we obtain optimality conditions for general non-convex constrained vector optimization problems. We apply thereafter the obtained pattern to a parametric quasiconvex programming problem for which we derive necessary and sufficient optimality conditions that are not sensitive to perturbation at the nominal level, yielding henceforth more – and strong at least under asymptotically regular constraints – information than the recent stability results obtained under additional conditions on the regularity of the normal cone to the adjusted sublevel sets of the underlying function.     

Continuity of the efficient solution mapping for vector optimization problems

This paper aims at investigating the continuity of the efficient solution mapping of perturbed vector optimization problems. First, we introduce the concept of the level mapping. We give sufficient conditions for the upper semicontinuity and the lower semicontinuity of the level mapping. The upper semicontinuity and the lower semicontinuity of the efficient solution mapping are established by using the continuity properties of the level mapping. We establish a corollary about the lower semicontinuity of the minimal point set-valued mapping. Meanwhile, we give some examples to illustrate that the corollary is different from the ones in the literature.     

Reinhardt域上一类推广的Roper-Suffridge算子

研究一类推广的Roper-Suffridge算子F(z)=(f(z_1)+f′(z_1)∑_(k=2)~nakz_k~pk,f′(z)1)(~1/p2)z_2,…,f′(z_1)~(1/pn)z_n)′,证明该算子在复欧氏空间中的Reinhardt域Ω_(n,p2,%…,pn)={z=(z_1,…,z_n)∈C~n:|z_|~2+∑_(k=2)~n|zk|~(pk)1,Pk∈N~+,k=2,…,n}上分别保持α次的殆β型螺形性,α次的β型螺形性及强β型螺形性.     

On the Hyers–Ulam stabilities of functional equations on ‐Banach spaces

The purpose of this article is to generalize the theory of stability of functional equations to the case of n‐Banach spaces. In this article, we prove the generalized Hyers–Ulam stabilities of the Cauchy functional equations, Jensen functional equations and quadratic functional equations on n‐Banach spaces.     

Noncompact‐type Krasnoselskii fixed‐point theorems and their applications

In this paper, we first establish some user‐friendly versions of fixed‐point theorems for the sum of two operators in the setting that the involved operators are not necessarily compact and continuous. These fixed‐point results generalize, encompass, and complement a number of previously known generalizations of the Krasnoselskii fixed‐point theorem. Next, with these obtained fixed‐point results, we study the existence of solutions for a class of transport equations, the existence of global solutions for a class of Darboux problems on the first quadrant, the existence and/or uniqueness of periodic solutions for a class of difference equations, and the existence and/or uniqueness of solutions for some kind of perturbed Volterra‐type integral equations. Copyright © 2015 John Wiley & Sons, Ltd.     

B~n上推广的Roper-Suffridge算子的性质

讨论改进后的Roper-Suffridge延拓算子保持双全纯映照子族的性质.借助双全纯映照子族的解析特征及其偏差结论,得到改进后的Roper-Suffridge延拓算子在一定条件下保持α次殆β型螺形映照、α次β型螺形映照、强β型螺形映照的性质,从而得到改进后的算子在一定条件下保持α次殆星形性、α次星形性和强星形性.所得结论为在多复变数空间中构造这些双全纯映照提供了一种新的途径.