Fixed Points of Nonexpansive Type Mappings in Topological Spaces

Recently. Penot[1] and Kirk[2]obtained the abstract versions of Kirk's fixed point theorem of [3] for nonexpansive mappings, respectively. Gille spie and Williams [4, 5] replaced the reflexive and normal structure used in Kirk [3] and Kannan [6], by uniformly normal structure to obtain the fixed point theorems for nonexpansive and Kannan mappings. Kaukich [7] also extended the result of [3] to the generalized nonexpansive mappings.     

G-凸空间内新的聚合不动点定理及应用

由应用连续单位分解技巧和Tychonoff不动点定理对定义在非紧G－凸空间的乘积空间上的一族集值映象证明了一些新的不动点定理。作为应用，对G－凸空间的乘积空间的一簇子集证明了Ky Fan型非空交定理；在G－凸空间内给出了非线性不等式组解的一个存在定理和得到了一些抽象经济的平衡存在定理，这些定理改进和推广了很多最近文献中重要的已知结果。     

RANDOM COMMON FIXED POINT THEOREMS OF SET-VALUED MAPPINGS

In this paper,we prove several random common fixed point theorems to general set-valued contractive mappings.These theorems improve and generalize the correspondingresults in[1-18].     

SOME RESULTS ON FIXED POINTS

In this paper,we first show several fixed point and or common fixed point theorems forpoint-vahied and set-valued contractive type mappings in compact metric spaces,whichsatisfy very general contractive condition with strict inequality and may be discontinuous.Our theorems improve and generalize some main results in[1—4].In the next place,we provide some new results for quite general orbitally contractionand quasi-contraction mappings.They improve,unify and extend some important resultsin[7—15].     

Maximal elements and generalized games involving condensing mappings in locally FC-uniform spaces and applications(Ⅱ)

This paper is a continuum of the preceding paper of author.Some new sys- tems of generalized vector quasi-equilibrium problems involving condensing mappings are introduced and studied in locally FC-uniform spaces.By applying the existence theorem of maximal elements of condensing set-valued mappings in locally FC-uniform spaces obtained by author in the preceding paper,some new existence theorems of solutions for the systems of generalized vector quasi-equilibrium problems are proved in locally FC- uniform spaces.These results improve and generalize some known results in literature to locally FC-uniform spaces.     

NEW COLLECTIVELY FIXED POINT THEOREMS AND APPLICATIONS IN G-CONVEX SPACES

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GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS IN LOCALLY G-CONVEX SPACES

IntroductionLetX ,YbetwotopologicalspacesandZbeanonemptyset.LetF∶X×X→ 2 Z,A∶X→ 2 XandC∶X→ 2 Zbeset_valuedmappingswhere2 ZdenotesthefamilyofallsubsetsofZ .　　Thegeneralizedvectorquasi_equilibriumproblemofType (Ⅰ ) (inshort,GVQEP(Ⅰ ) )istofind ^x∈Xsuchthat^x∈A( ^x)andF( ^x ,z) C( ^x) ,　　 z∈A( ^x) . ( 1 )　　Thegeneralizedvectorquasi_equilibriumproblemofType (Ⅱ ) (inshort,GVQEP(Ⅱ ) )istofind ^x∈Xsuchthat^x∈A( ^x)andF( ^x ,z) C( ^x) ,　　 z∈A( ^x) . ( 2 )　　…     

SYSTEM OF COINCIDENCE THEOREMS IN PRODUCT TOPOLOGICAL SPACES AND APPLICATIONS (Ⅱ)

By applying coincidence theorems in part (Ⅰ) for two families of set-valued mappings defined on product space of noncompact FC-spaces in preceding paper, some new existence theorems for system of vector equilibrium problems, system of inequalities and system of minimax theorems were established in FC-spaces. These results generalize some known results in recent literature.     

SOME COINCIDENCE THEOREMS OF SET-VALUED MAPPINGS

Browder[1]obtained the sharpend forms of the Schauder fixed point theorem.Manyauthors generalized Browder’s results in several aspects.Recently,H.M.Ko and K.K.Tan[2,3]generalized Browder’s theorems to the coincidence theorems of set-valuedmappings.In this paper,we also show some coincidence theorems of set-valued mappings.They improve and generalize the important results in[1,2,3].     

GENERAL RANDOM FIXED POINT THEOREM AND ITS APPLICAT1ONS

In this paper, we obtain a general random fixed point theorem which generalizes the main results of Engle and Bocsan. The usefulness of this theorem seems to lie in the fact that unlike many random fixed point theorems obtained by using special methods can be proved by using out general theorem (Theorem 1 and Corollaries 1 and 2). Finally, we indicate some possible applications of our results to nonlinear random integral and differential equations.