Harmonic mappings of the hexagasket to the circle

Harmonic mappings from the hexagasket to the circle are described in terms of boundary values and topological data.Explicit formulas are also given for the energy of the mapping.We have generalized the results in [10].     

半模糊凸模糊映射

In this paper, a new class of fuzzy mappings called semistrictly convex fuzzy mappings is introduced and we present some properties of this kind of fuzzy mappings. In particular, we prove that a local minimum of a semistrictly convex fuzzy mapping is also a global minimum. We also discuss the relations among convexity, strict convexity and semistrict convexity of fuzzy mapping, and give several sufficient conditions for convexity and semistrict convexity.     

Fixed Point Theorems of the Iterated Function Systems

In this paper, we present some fixed point theorems of iterated function systems consisting of α-ψ-contractive type mappings in Fractal space constituted by the compact subset of metric space and iterated function systems consisting of Banach contractive mappings in Fractal space constituted by the compact subset of generalized metric space, which is also extensively applied in topological dynamic system.     

抽象凸空间中集值映射的不动点定理及其应用

A new fixed point theorem and the selection property for upper semi-continuous set-valued mappings in abstract convexity space are established. As their applications the existence of Nash equilibrium for n-person non-cooperative generalized games is proved.     

On the Generalized Topological Degree for Perturbed Maximal Monotone Mappings

In recent years, F.E. Browder has constructed the topological degree for nonlinear monotone mappings.In the paper[1], we have introduced the classes of mappings of type (S)_ ~* and of type quasi-(S)_ ~* and the concept of weakly-demicontinuity and we have constructed the generalized topological degree for these classes of mappings. Some important results in [2] and [3] have     

A Fixed Point Theorem and Some Generalized Ky Fan＇s Minimax Inequalities

In this paper, we establish a fixed point theorem for set-valued mapping on a topological vector space without ＂local convexity＂. And we also establish some generalized Ky Fan＇s minimax inequalities for set-value vector mappings, which are the generalization of some previous results.     

New fixed point theorems for <Emphasis Type="Italic">P</Emphasis><Subscript>1</Subscript>-compact mappings in Banach spaces

E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn, we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder＇s theorem, Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem, etc.     

A REMARK ON THE DERIVATE OF SET-VALUED MAPPING

The derivate of set-valued mappings was defined by Hakuhara M in [1] and is called H-derivate. This paper shows a necessary and sufficient condition for a set-valued mapping to be derivable in term of Hderivate and the conditions in which lirnit and derivate ,derivate and integyal are exchanged respectively.     

On the Refined Esitmates of All Homogeneous Expansions for a Subclass of Biholomorphic Starlike Mappings in Several Complex Variables

The refined estimates of all homogeneous expansions for a subclass of biholomorphic starlike mappings are mainly established on the unit ball in complex Banach spaces or the unit polydisk in Cn with a unified method. Especially the results are sharp if the above mappings are further k-fold symmetric starlike mappings or k-fold symmetric starlike mappings of order α. The obtained results unify and generalize the corresponding results in some prior literatures.     

增生映射的扰动理论对与广义(p,q)-Laplace算子相关的非线性椭圆系的应用

Using perturbation results on the sums of ranges of nonlinear accretive mappings of Calvert and Gupta, we present some abstract results for the existence of the solutions of nonlinear Neumann elliptic systems which is related to the so-called generalized （p, q）-Laplacian in this paper. The systems discussed in this paper and the method used extend and complement some of the previous work.     

The Derived Mappings and the Order of a Set-Valued Mapping Between Topological Spaces

Previous investigations of, in particular, continuous selections have led to the definition of the derived mappings and, here, the order of a set-valued mapping between topological spaces. The relation between the topological spaces and the possible orders of set-valued mappings between them is considered and examples are constructed to show that each ordinal number is the order of some set-valued mapping.     

On Generalized Vector Equilibrium Problems

A new generalized vector equilibrium problem involving set-valued mappings and the proper quasi concavity of set-valued mappings in topological vector spaces are introduced; its existence theorems and the convexity of the solution sets are established.     

拓扑空间中一些新的不动点定理

介绍了我们在不动点定理方面的一些最新结果，包括：拓扑空间中Meir-Keeler型映象的不动点定理，有序拓扑空间中增算子和多值增映射的不动点定理，拓扑空间中压缩映象的不动点定理和多值映象的公共不动点定理。甚至在通常的度量空间，所有这些结果也是新的。     

方向导数和广义锥-预不变凸集值优化问题

讨论拓扑向量空间中无约束集值优化问题的最优性条件问题.利用集值映射的Dini方向导数,在广义锥-预不变凸性条件下,建立了集值优化问题关于弱极小元和强极小元的最优性充分必要条件.     

Coincidence Theorems with Applications to Minimax Inequalities, Section Theorem, Best Approximation and Multiobjective Games in Topological Spaces

Some new coincidence theorems involving admissible set-valued mappings are proved in general noncompact topological spaces. As applications, some new minimax inequalities, section theorem, best approximation theorem, existence theorems of weighted Nash equilibria and Pareto equilibria for multiobjective games are given in general topological spaces.     

一类集值映像方程的解及其应用

讨论局部凸拓扑向量空间中集值K映象方程解的存在性,并给出了在微分方程上的一个应用.     

Selections and selectors

The aim of the paper is to outline the known results and the main technics they are obtained with as well as the open questions about selections of set-valued mappings. More precisely the following topics will be touched: Set-valued selections of set-valued mappings, factorizations of set-valued mappings, inverse selection theorems, selections via extension of the set-valued mapping.     

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.     

Nonconvex vector optimization of set-valued mappings

In this paper, we discuss properties, such as monotonicity and continuity, of the Gerstewitz's nonconvex separation functional. With the aid of this functional, necessary and sufficient optimality conditions for nonconvex optimization problems of set-valued mappings are obtained in topological vector spaces.     

A Fixed Point Theorem and Some Generalized Ky Fan's Minimax Inequalities

In this paper, we establish a fixed point theorem for set-valued mapping on a topological vector space without "local convexity". And we also establish some generalized Ky Fan's minimax inequalities for set-value vector mappings, which are the generalization of some previous results.