集值邻近连续映射

关于单值邻近连续映射的概念及性质已为人们所熟知,而研究集值邻近连续映射的论文至今尚未见到.本文给出了集值邻近连续映射和上、下半弱集值邻近连续映射的定义、判定条件和它们之间的关系.最后,研究了上(下)半弱集值邻近连续映射与众所周知的上(下)半集值连续映射之间的关系.从而得到了集值邻近连续映射与已知的集值连续映射之间的关系.     

集值映射的拓扑收敛

本文通过例子和定理证明:仅在一定条件下,集值映射网的拓扑收敛与其两种常见的收敛(点态收敛及一致收敛)方能比较。     

集值映射的拟一致收敛

本文中，在拟一致空间中引入强局部对称性的概念，并讨论集值映射的拟一致收敛性．本文推广了［５］中的一些结果，同时用反例否定了［３］和［４］中的主要定理     

欧氏空间的集值映射不动点

本文通过取凸包与闭包,利用关系正常法,Lebesgue测度和均匀连续映射,讨论欧氏空间的集值映射的不动点,获得了一些结果.     

集值映射空间上的基数函数

讨论了集值映射空间在赋予点态收敛拓扑或紧开拓扑下的权数,特征,网络权,稠密度等基数函数,利用自然映射,诱导映射和嵌入等方法将单值连续映射空间的有关结论推广到集值映射空间类上.     

集值映射与不动点

应用D关于β对应关系是正常的构架,引用子集法,通过取凸包与闭包,由单值映射构造集值映射,利用Kakutani不动点定理,讨论几种类型的集值映射的不动点.     

集值映射空间上的自然映射(英文)

In this paper,we discuss the continuities of some natural mappings on pointcompact continuous set-valued mapping spaces with compact-open topology and obtain the properties of set-valued injective mappings,set-valued diagonal mappings,induced mappings,set-valued evaluation mappings,set-valued topological sum mappings and set-valued topological product mappings.     

锥拟凸集值映射与集值映射的锥半连续性

本文借助锥界集定义了一种新的锥拟凸集值映射,并且利用广义Minkowski泛函讨论了锥半连续及锥外上半连续集值映射的锥拟凸性．     

集值映射的连续性

本文将单值映射Γ:X→Y连续的一种充要条件: (?)(Γ~(-1)(B))(?)Γ~-((?)B),(?)B(?)Y推广到集值映射的情形,然后讨论了Banach空间X中有界线性算子T∈B(X)的谱σ(T)当B(X)赋以一致拓扑时的连续性,得出了σ(T)在任意M(?)B(X)上连续的充要条件,当M=B(X)或σ(T)不在全M上连续时,此条件也是σ(T)在B(X)或M中某点处连续的充要条件。     

内积空间中的h-强凸集值映射

本文首先在赋范线性空间中引入一类广义强凸集值映射,称之为h-强凸集值映射.其次利用R?dstr?m消去律研究了h-强凸集值映射的一些基本性质.最后,给出h-强凸集值映射形式下赋范线性空间为内积空间的刻画条件.     

取值为Banach空间的集值映射的非线性逼近

本文研究了取值为Ｂａｎａｃｈ空间中的集的集值映射的非线性逼近问题．给出集值映射的最佳逼近的特征和唯一性定理，并刻划了使其特征定理成立的非线性类的特征．     

集值映射的次微分以及最优性条件

基于已有的集值映射的弱次微分的概念,定义了集值映射的Henig全局次微分,研究了它的存在性条件以及运算性质．利用这一概念,分别给出了具约束向量集值最优化问题的Henig全局有效解对的必要性条件和充分性条件．     

Topological Stability and Entropy for Certain Set-valued Maps

In this paper,the dynamics(including shadowing property,expansiveness,topological stability and entropy) of several types of upper semi-continuous set-valued maps are mainly considered from differentiable dynamical systems points of view.It is shown that(1) if f is a hyperbolic endomorphism then for each ε> 0 there exists a C¹-neighborhood U of f such that the induced set-valued map F_f,U has the ε-shadowing property,and moreover,if f is an expanding endomorphism then the...     

Existence Theorems for Set-valued Operators in Banach Spaces

In this paper, we study the problem of existence of zero points for set-valued operators in Banach spaces. We present a simple condition which can be used to verify that under some conditions, set-valued operators have zero points. Furthermore, we derive the surjectivity result and the Kakutani fixed point theorem by using this condition.      

An Improvement of Existence Theorems of Additive Selection Maps for Sub-additive Set-valued Maps

In this paper, we will construct a new class of subadditive set-valued maps and use Cantor theorem to prove that the set-valued map has an unique additive selection map when the set-valued map satisfies some certain conditions, and then compare the obtained result with the well-known results.     

Dual Convergences of Iteration Processes for Nonexpansive Mappings in Banach Spaces

In this paper we establish a dual weak convergence theorem for the Ishikawa iteration process for nonexpansive mappings in a reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm, and then apply this result to study the problem of the weak convergence of the iteration process.     

The Convergences of Bivariate Integral Jackson Interpolating Operators in Orlicz Spaces

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About Semicontinuity of Set-valued Maps and Stability of Quasivariational Inclusions

We propose several additional kinds of semi-limits and corresponding notions of semicontinuity of a set-valued map. They can be used additionally to known basic concepts of semicontinuity to have a clearer insight of local behaviors of maps. Then, we investigate semicontinuity properties of solution maps to a general parametric quasivariational inclusion, which is shown to include most of optimization-related problems. Consequences are derived for several particular problems. Our results are new or generalize/improve recent existing ones in the literature.     

集值映射的广义梯度和全局真有效解

本文利用集值映射的上图导数引进了全局真有效意义下的广义梯度和广义次微分的概念，并且给出了集值映射全局真有效次微分的存在定理，还建立了集值向量优化问题全局真有效解在次微分形式下的最优性条件．