Modified continuity and a generalisation of Michael's selection theorem

We modify the definitions of continuity and lower semicontinuity for single-valued mappings and upper and lower semicontinuity for set-valued mappings. For single-valued mappings we have a generalisation of Osgood's theorem and for set-valued mappings we have an extension of Fort's theorem and a generalisation of Michael's selection theorem producing a densely defined selection with a natural continuity property relative to the domain.     

Fuzzy selection and existence of fuzzy fixed point

In this paper, we shall prove a new fuzzy continuous selection theorem in a compact convex set and next a fixed point theorem for fuzzy mappings is established.     

Continuous selections for set-valued mappings with finite-dimensional convex values

We show selection theorems for set-valued mappings with finite-dimensional convex values, one of which is a partial extension of a selection theorem due to S. Barov (2008) [1].     

Brouwer-Schauder-Tychonoff不动点定理的进一步推广

最近,Wu和Yuan将Brouwer-Schauder-Tychonoff不动点定理推广到H-空间.本文首先建立一个逼近选择定理,然后使用这个结果建立一个新的不动点定理,很大地改进和推广了Wu和Yuan的结果.     

A selection theorem for quasi-lower semicontinuous mappings in hyperconvex spaces

We prove a continuous selection theorem for quasi-lower semicontinuous mappings with values that are closed sub-admissible subsets of a hyperconvex metric space and apply this result to obtain fixed point theorems in these spaces.     

关于下半连续集值映射的一个定理

本文研究了取值于可展空间内的集值映射的选择问题，得到了下半连续映射的一个选择定理。     

乘积拓扑空间内的重合点组定理及应用(Ⅰ)

首先引入了无凸性结构的有限连续拓扑空间(简称FC-空间)新概念．其次在FC-空间内建立了一个新的连续选择定理．应用此定理,在很弱的假设下,对定义在非紧FC-空间的乘积空间上的两个集值映射簇证明了某些新的重合点定理．这些结果推广了最近文献中的许多已知结果．某些应用将在后继文章中给出．     

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.     

对Aubin与Frankowska关于闭凸集值映射最小选择的一个结果的讨论

本文对Ｊ．－Ｐ．Ａｕｂｉｎ与Ｈ．Ｆｒａｎｋｏｗｓｋａ最近关于自反严格凸Ｂａｎａｃｈ空间中闭凸集值映射最小选择连续的于个结果加以讨论,首先在比自反性较强的一类空间中讨论了在弱ｕｂｉｎ与Ｈ．Ｆｒａｎｋｏｗｓｋａ的条件下闭凸集值映射最小选择的连续性,其次对Ｊ．Ｐ．Ａｕｂｉｎ与Ｈ．Ｆｒａｎｋｏｗｓｋａ的结果给出了一个新的简单证明,最后用反例说明本文给出的条件Ｊ．Ｐ．Ａｕｂｉｎ与Ｈ．Ｆｒａｎｋｏｗｓａｋａ条     

Multivalued fixed point in Banach algebra using continuous selection and its application to differential inclusion

In this paper, we provide some fixed point results using continuous selection given by Poonguzali et al. [15]. Also, using the selection theorem we discusse the existence of fixed point for the product of two multivalued mappings, that is, of the form $Ax\cdot Bx.$ Using those fixed point results, we give the existence of solution for a newly developed differential inclusion.     

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 Bartle-Graves theorem

The Bartle-Graves theorem extends the Banach open mapping principle to a family of linear and bounded mappings, thus showing that surjectivity of each member of the family is equivalent to the openness of the whole family. In this paper we place this theorem in the perspective of recent concepts and results, and present a general Bartle-Graves theorem for set-valued mappings. As applications, we obtain versions of this theorem for mappings defined by systems of inequalities, and for monotone variational inequalities.

     

一类近于凸映照子族精确的偏差定理

首先建立了C~n中单位多圆柱上一类近于凸映照子族精确的偏差定理,同时在复Banach空间单位球上也建立了该类映照精确的偏差定理的下界估计.其次在复Banach空间单位球上建立了准星形映照精确的偏差定理.所得结果将单复变中近于凸函数和星形函数的偏差定理推广至高维情形,并且对龚升提出的一个公开问题给出肯定的回答.     

On a conjecture of S. Reich

Simeon Reich (1974) proved that the fixed point theorem for single-valued mappings proved by Boyd and Wong can be generalized to multivalued mappings which map points into compact sets. He then asked (1983) whether his theorem can be extended to multivalued mappings whose range consists of bounded closed sets. In this note, we provide an affirmative answer for a certain subclass of Boyd-Wong contractive mappings.

     

拓扑空间中Fan-Browder映射的连续选择定理及其应用

首先,在不具有任何凸性结构的拓扑空间中引入Fan-Browder映射的概念．然后,证明了一个新的关于Fan-Browder映射的连续选择定理,其中定义域是非紧的,值域是不具有任何凸性结构的拓扑空间的子集．作为应用,给出了一些不动点定理、叠合点定理和一个非空交定理．这些新的概念和定理统一和推广了许多已有的结果．     

Fuzzy mappings and fixed point theorems

We extend Heilpern's fixed point theorem for fuzzy contraction mappings to a pair of generalized fuzzy contraction mappings. Also we prove a fixed point theorem for nonexpansive fuzzy mappings on a compact star-shaped subset of a Banach space.     

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.     

多复变数全纯映射精细的Bohr定理

本文首先建立不依赖自同构从复Banach空间平衡域到Cn单位多圆柱上一定限制条件下全纯映射精细的范数型Bohr定理及复Banach空间X上单位球到复Banach空间Y上单位球全纯映射精细的泛函型Bohr定理.其次,给出有界对称域上全纯映射精细的Bohr定理.最后,得到J*代数单位球上全纯映射精细的Bohr定理.所得结果将一维的Bohr定理推广至高维.     

Selections for paraconvex-valued mappings on non-paracompact domains

We prove that Michael?s paraconvex-valued selection theorem for paracompact spaces remains true for C^′(E)-valued mappings defined on collectionwise normal spaces. Some possible generalisations are also given.     

Compatible mappings of type (B) and common fixed point theorems in Saks spaces

In this paper we first introduce the concept of compatible mappings of type (B) and compare these mappings with compatible mappings and compatible mappings of type (A) in Saks spaces. In the sequel, we derive some relations between these mappings. Secondly, we prove a coincidence point theorem and common fixed point theorem for compatible mappings of type (B) in Saks spaces.