Fixed Point Theorems on a Non-convex Set

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Banach空间中多类1-集-压缩映象的逼近定理和不动点定理

本文证明了 Ｋｙ Ｆａｎ定理［１］对定义在 Ｂａｎａｃｈ空间中含有内点的有界闭凸子集上的１－集－压缩映象正确．１－集－压缩映象类包含凝聚映象、非扩张映象、半压缩映象、局部几乎非扩张映象和其它映象．作为定理的应用,得到了一些非自映象在许多众知边界条件下的不动点定理,改进和推广了许多作者的最近结果．     

Approximation Theorems and Fixed Point Theorems for Various Classes of 1-set-contractive Mappings in Banach Spaces

In this paper, we will prove that Ky Fan's Theorem (Math. Z. 112(1969), 234–240) is true for 1-set-contractive maps defined on a bounded closed convex subset K in a Banach space with intK≠0. This class of 1-set-contractive maps includes condensing maps, nonexpansive maps, semicontractive maps, LANE maps and others. As applications of our theorems, some fixed point theorems of non-selfmaps are proved under various well-known boundary conditions. Our results are generalizations and improvements of the recent results obtained by many authors. Project supported by the National Natural Science Foundation of China and Natural Science Foundation of Shandong Province of China     

PM-空间中混合压缩的不动点定理与重合点定理

引进了Menger PM-空间中多值情形下的相容映象和弱相容映象概念，并研究了二者之间的联系．在此基础上，获得了Menger PM-空间中若干新的不动点和重合点定理．最后，给出了这一结果在度量空间中的应用．     

局部凸拓扑向量空间中的不动点定理

本文在局部凸拓扑向量空间中得到了几个新的不动点定理，推广了［２］中的几个重要结果．     

锥度量空间中的不动点定理

本文首先在锥度量空间中引入了ψ序压缩算子这一概念,然后证明了几个ψ-序压缩算子的不动点存在性定理.     

非紧非单调算子的不动点定理

本文利用和选择公理等价的Zorn引理,得到了一般非单调算子不动点存在性的一些结果.     

Fixed Point Theorems and Convergence Theorems for a New Generalized Nonexpansive Mapping

Abstract

This paper introduces a new mapping that is weaker than nonexpansive mapping. The new mapping is different from the Suzuki’s generalized nonexpansive mapping. This paper introduces a new iteration process for the fixed point, and gives fixed point theorems and Convergence theorems for a new generalized nonexpansive mapping in Banach space, insteading of uniformly convex Banach space.     

Fixed Point Theorems for Increasing Operators of None－continuity and None－compactness Conditions

ＦｉｘｅｄＰｏｉｎｔＴｈｅｏｒｅｍｓｆｏｒＩｎｃｒｅａｓｉｎｇＯｐｅｒａｔｏｒｓｏｆＮｏｎｅ－ｃｏｎｔｉｎｕｉｔｙａｎｄＮｏｎｅ－ｃｏｍｐａｃｔｎｅｓｓＣｏｎｄｉｔｉｏｎｓＺｈａｎｇＱｉｎｇｚｈｅｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，...     

稳定Banach空间上的不动点定理

本文以超幂技术证明了具有单调无条件基的稳定Ｂａｎａｃｈ空间Ｘ有不动点性。     

Common Fixed Point Theorems in Complex Valued Metric Spaces

We introduce complex valued metric spaces and obtain sufficient conditions for the existence of common fixed points of a pair of mappings satisfying contractive type conditions.     

极大点空间的若干特征定理

本文利用极大点空间的等价刻划证明了极大点空间的某些子空间、不交和、 乘积空间、逆序列的逆极限、具有可数基的局部紧的Hausdorff空间是极大点空间,还 给出了具有可数基的局部紧的Hausdorff空间的Domain hull.     

Generalized Motzkin Theorems of the Alternative and Vector Optimization Problems

In this paper, we introduce a definition of generalized convexlike functions (preconvexlike functions). Then, under the weakened convexity, we study vector optimization problems in Hausdorff topological linear spaces. We establish some generalized Motzkin theorems of the alternative. By use of these theorems of the alternative, we obtain some Lagrangian multiplier theorems. A saddle-point theorem and a scalarization theorem are also derived.Communicated by F. GiannessiThe author thank Ginndomenico Mastrocni for helpful and useful comments.     

半序度量空间中单调映射的不动点定理及混合单调映射的耦合不动点定理

本文在度量空间中引入半序,证明了半序度量空间中单调增加映射的不动点定理及混合单调映射的耦合不动点定理．     

u0 - 凹算子的不动点定理及其应用

该文利用锥的性质和单调迭代技巧讨论了u₀ - 凹算子正不动点的存在唯一性,所得结论改进并推广了已有的相关结果. 作为应用, 该文研究了一类Hammerstein积分方程正解的存在唯一性.     

凸度量空间中单值和集值映象的公共不动点定理

§ 1.　Introduction　　Anecessaryandsufficientconditionandasufficientconditiontoensurethataset valuedmappingandasingle valuedmappinginacompletemetricspaceandacompleteconvexmetricspacehavingacommonfixedpointarerespectivelygivenin [1 ] .Meanwhilethemainresultsin[2 ]— [5]areimprovedandextendedin [1 ] .Inthispaper ,theexistenceatcommonfixedpointsoftwoset valuedmappingandasing valuedmappingwerestudied ,andthecorrespond ingresultsin [1 ]— [5]wereextendedandimproved .Let(X ,d)beanon emptymetricspa…     

Banach空间中多值映象的不动点定理

本文中我们首先证明了一个不动点定理，同时从压缩及弱内向两个方向推广了压缩弱内向映象的不动点定理［１，２］．在后两节中讨论了Ｂａｎａｃｈ空间中无界闭子集上的不动点定理，所得结果推广了［３，４］中相应定理．     

Fixed Point Theorems for Mean Nonexpansive Mappings in CAT(0) Spaces

In this article, we prove the existence of fixed points and the demiclosed principle for mean nonexpansive mappings in Cartan, Alexandrov and Toponogov(0) spaces. We also obtain a Δ-convergence theorem and a strong convergence theorem of Ishikawa iteration for mean nonexpansive mappings in Cartan, Alexandrov and Toponogov(0) spaces.     

Quasi-Equilibrium Problems and Fixed Point Theorems of Separately l.s.c and u.s.c Mappings

In this paper, we apply our new results on quasi-variational inequality problems to generalized quasi-equilibrium problems. Some su?cient conditions on the existence of solutions are shown. In particular, we establish several results on the existence of solutions to fixed points of separately lower and upper semicontinuous (lower and lower, upper and upper) mappings.These generalize some well-known fixed point theorems obtained by previous authors as Browder and Ky Fan, Wu, et al., etc.     

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。