拓扑向量空间中锥半连续性与锥拟凸映射

对于拓扑向量空间中的几个锥拟凸映射,讨论了它们之间的若干关系,同时,对锥半连续及锥上半连续映射的锥拟凸性给出了一些结果。     

New Results on Generalized $c$-Distance Without Continuity in Cone $b$-Metric Spaces over Banach Algebras

In this work, some new fixed point results for generalized Lipschitz mappings on generalized $c$-distance in cone $b$-metric spaces over Banach algebras are obtained, not acquiring the condition that the underlying cone should be normal or the mappings should be continuous. Furthermore, the existence and the uniqueness of the fixed point are proven for such mappings. These results greatly improve and generalize several well-known comparable results in the literature. Moreover, some examples and an application are given to support our new results.     

Subdifferential of Optimal Value Functions in Nonlinear Infinite Programming

This paper presents an exact formula for computing the normal cones of the constraint set mapping including the Clarke normal cone and the Mordukhovich normal cone in infinite programming under the extended Mangasarian-Fromovitz constraint qualification condition. Then, we derive an upper estimate as well as an exact formula for the limiting subdifferential of the marginal/optimal value function in a general Banach space setting.     

Common Fixed Point Theorems and Q-prop erty for Quasi-contractive Mappings under c-distance on TVS-valued Cone Metric Spaces without the Normality

Fixed point and common fixed point results for mappings satisfying quasi-contractive conditions expressed in the terms of c-distance on TVS-valued cone met-ric spaces (without the underlying cone which is not normal) are obtained, and P-property and Q-property for mappings in the terms of c-distance are discussed. Our results generalize and improve many known results.     

Distortion theorems for subclasses of starlike mappings along a unit direction in ℂ

In this paper, we obtain a distortion theorem of Jacobian matrix for biholomorphic subclasses of starlike mappings along a unit direction on the unit polydisc. These results extend the classical distortion theorem of starlike mappings to higher dimensions. We then give an upper bound estimate for biholomorphic subclasses of starlike mappings along a unit direction in a complex Banach space.     

Denjoy-Wolff theorems for Hilbert’s and Thompson’s metric spaces

We study the dynamics of fixed point free mappings on the interior of a normal, closed cone in a Banach space that are nonexpansive with respect to Hilbert’s metric or Thompson’s metric. We establish several Denjoy-Wolff type theorems which confirm conjectures by Karlsson and Nussbaum for an important class of nonexpansive mappings. We also extend and put into a broader perspective results by Gaubert and Vigeral concerning the linear escape rate of such nonexpansive mappings.     

Optimality conditions for vector optimization problem governed by the cone constrained generalized equations

ABSTRACT

The paper considers a class of vector optimization problems with cone constrained generalized equations. By virtue of advanced tools of variational analysis and generalized differentiation, a limiting normal cone of the graph of the normal cone constrained by the second-order cone is obtained. Based on the calmness condition, we derive an upper estimate of the coderivative for a composite set-valued mapping. The necessary optimality condition for the problem is established under the linear independent constraint qualification. As a special case, the obtained optimality condition is simplified with the help of strict complementarity relaxation conditions. The numerical results on different examples are given to illustrate the efficiency of the optimality conditions.     

Upper and Lower Semicontinuity for Set-Valued Mappings Involving Constraints

In vector optimization, several authors have studied the upper and lower semicontinuity for mappings involving constraints in topological vector spaces partially ordered through a cone with nonempty interior. In this paper, we give conditions about the upper and lower semicontinuity in the case that the ordering cone in the parameter space has possibly empty interior, as it happens in many function spaces and seqence spaces.     

Estimates of a spectrum of the integral means for lacunary series

We obtain an upper estimate for the integral means spectrum of conformal mappings generated by the Hadamard lacunary power series with a lacunarity index 2.     

法向锥与集值映射的单调极大性

研究局部凸空间凸集的法向锥及单调映射与下半连续凸函数的次微分之和的单调极大性．并讨论集值映射循环单调的极大性．     

多复变数星形映射在某方向上精确的偏差定理

研究了Cn中单位多圆柱上星形映射在某方向上精确的偏差定理．给出了复Banach空间单位球的某方向上精确的偏差的上界,同时给出了下界的猜测．     

Minimax Problems for Set-Valued Mappings

In this article, by virtue of the Fan-Browder fixed point theorem, we first obtain a minimax theorem and establish an equivalent relationship between the minimax theorem and a cone saddle point theorem for scalar set-valued mappings. Then, by using scalarization functions, we investigate an existence theorem of the cone saddle point for set-valued mappings. Simultaneously, we also establish a minimax theorem for set-valued mappings.     

On the sharp upper bound for the number of holomorphic mappings of Riemann surfaces of low genus

We obtain an upper bound for the number of holomorphic mappings of a genus 3 Riemann surface onto a genus 2 Riemann surface in a series of cases. In particular, we establish that the number of holomorphic mappings of an arbitrary genus 3 Riemann surface onto an arbitrary genus 2 Riemann surface is at most 48. We show that this estimate is sharp and find pairs of Riemann surfaces for which it is attained.     

半序锥度量空间中新公共不动点定理(英文)

该文在半序锥度量空间中研究了有关三个映射的公共不动点的存在唯一性,不要求映射的连续性和交换性,也不要求锥的正规性,其结果改进并推广了文献中的一些重要结论.     

Exact Formulae for Coderivatives of Normal Cone Mappings to Perturbed Polyhedral Convex Sets

In this paper, without using any regularity assumptions, we derive a new exact formula for computing the Fréchet coderivative and an exact formula for the Mordukhovich coderivative of normal cone mappings to perturbed polyhedral convex sets. Our development establishes generalizations and complements of the existing results on the topic. An example to illustrate formulae is given.     

不具有关于锥的例外簇的映射

给出Hilbert空间到其自身不具有关于锥的例外族的映射条件，利用Hilbert空间可表为闭凸锥与负对偶锥的特点研究映射关于锥的例外簇的特性，证明了可通过映射在某紧凸子集上的性态判断其例外簇的存在与否，并讨论单调和沿射线单调映射的不具例外簇问题。     

Remarks on “Quasi-contraction on a cone metric space”

Recently, D. Ili? and V. Rako?evi? [D. Ili?, V. Rako?evi?, Quasi-contraction on a cone metric space, Appl. Math. Lett. (2008) doi:10.1016/j.aml.2008.08.011] proved a fixed point theorem for quasi-contractive mappings in cone metric spaces when the underlying cone is normal. The aim of this paper is to prove this and some related results without using the normality condition.     

锥度量空间上在$c$-距离下Lipschitz型映射的唯一公共不动点定理

在本文,给出了正规的锥度量空间上在$c$-距离下满足Lipschitz型条件的四个映射的唯一公共不动点定理.所得结果推广和改进了很多已知的公共不动点定理.     

广义强向量拟平衡问题解的存在性和Hadamard适定性

首先,在映射－f(·,y,u)自然拟C-凸和映射f上半(－C)-连续的条件下,构造一个重要辅助函数,利用不同的证明方法,在不要求C*具有弱*紧基的情况下,建立了广义强向量拟平衡问题解的存在性定理.然后在适当条件下,给出问题序列收敛的定义,建立解集映射的上半连续性,并讨论广义强向量拟平衡问题的Hadamard适定性,得到广义强向量拟平衡问题的Hadamard适定性成立的充分条件.     

锥b-Banach空间上非扩张映射的不动点定理

在锥b-Banach空间上考虑多个映射的公共不动点问题,利用Mann迭代法以及锥b-范数的条件下证明锥b-Banach空间上多个映射的公共不动点的存在性.