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GENERALIZED VECTOR VARIATIONAL-TYPE INEQUALITIES IN fc-spaceS

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Applied Mathematics and Mechanics(English Edition) 2006年第11期27卷 1451-1459页

作者：方敏丁协平 College of Mathematics Sichuan UniversityChengdu 610064P. R. China College of Mathematics and Software Science Sichuan Normal UniversityChengdu 610066P. R. China

A class of generalized vector variational-type inequality problems （GVVTIP） are studied in fc-spaces, which includes the most of vector equilibrium problems, vector variational inequality problems, generalized vector equilibrium problems and general- ized vector variational inequality problem as special cases. By using F-KKM theorem, some new existence results for GVVTIP axe established in noncompact fc-space. As consequences, some recent known results in literature are obtained under much weaker assumption.

关键词： generalized vector variational-type inequality F-KKM mapping F-Px-diagonally quasiconvex fc-space

MATHEMATICAL PROGRAMS WITH SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM CONSTRAINTS IN fc-spaceS

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Acta Mathematica Scientia 2010年第4期30卷 1257-1268页

作者：丁协平 College of Mathematics and Software Science Sichuan Normal University Chengdu

In this article, four new classes of systems of generalized vector quasi-equilibrium problems are introduced and studied in fc-spaces without convexity structure. The notions of Ci（x）-fc-partially diagonally quasiconvex, Ci（x）-fc-quasiconvex, and Ci（x）-fc- quasiconvex-like for set-valued mappings are also introduced in fc-spaces. By applying these notions and a maximal element theorem, the nonemptyness and compactness of solution sets for four classes of systems of generalized vector quasi-equilibrium problems are proved in noncompact fc-spaces. As applications, some new existence theorems of solutions for mathematical programs with system of generalized vector quasi-equilibrium constraints are obtained in fc-spaces. These results improve and generalize some recent known results in literature.

关键词： Maximal element system of generalized vector quasi-equilibrium problems Mathematical program Ci(x)-fc-partially diagonally quasiconvex Ci(x)-fc-quasiconvex Ci(x)-fc-quasiconvex-like fc-space

ON COLLECTIVELY FIXED POINT THEOREMS ON fc-spaceS

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Analysis in Theory and Applications 2010年第3期26卷 228-235页

作者： Yongjie Piao Yanbian University China

Based on a KKM type theorem on fc-space, some new fixed point theorems for Fan-Browder type are established, and then some collectively fixed point theorems for a family of Ф-maps defined on product space of fc-space... 详细信息

关键词： fc-space fc-subset KKM map Ф-map collectively fixed point

Coincidence Point Theorems,Intersection Theorems and Saddle Point Theorems on fc-spaces

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Communications in Mathematical Research 2009年第2期25卷 115-122页

作者： PIAO YONG-JIE YIN ZHE Department of Mathematics Yanbian University Yanji Jilin 133002

In this paper, we first give the definitions of finitely continuous topological space and fc-subspace generated by some set, and obtain coincidence point theorem, whole intersection theorems and Ky Fan type matching t... 详细信息

关键词： fc-space fc-subspace generated by set saddle point

Continuous Selection,Collectively Fixed Points and System of Coincidence Theorems in Product Topological spaces

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Acta Mathematica Sinica,English Series 2006年第6期22卷 1629-1638页

作者： Xie Ping DING College of Mathematics and Software Science Sichuan Normal University Chengdu 610066 P. R. China

Some new continuous selection theorems are first proved in noncompact topological spaces. As applications, some new collectively fixed point theorems and coincidence theorems for two families of set-valued mappings defined on product space of noncompact topological spaces are obtained under very weak assumptions. These results generalize many known results in recent literature.

关键词： continuous selection collectively fixed point coincidence theorem for two families of set-valued mappings fc-space

SYSTEM OF COINCIDENCE THEOREMS IN PRODUCT TOPOLOGICAL spaceS AND APPLICATIONS (Ⅰ)

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Applied Mathematics and Mechanics(English Edition) 2005年第12期26卷 1547-1555页

作者：丁协平 College of Mathematics and Software Science Sichuan Normal University

A new notion of finite continuous topological space（in short, fc-space） with out convexity structure was introduced. A new continuous selection theorem was established in fc-spaces. By applying the continuous selection theorem, some new coincidence theorems for two families of set-valued mappings defined on product space of noncompact fc-spaces are proved under much weak assumptions. These results generalize many known results in recent literature. Some applications will be given in a follow-up paper.

关键词： system of coincidence theorems continuous selection transfer compact open value fc-space

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Continuous Selections and Fixed Points forφ-maps with Their Applications to Section Problems

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Communications in Mathematical Research 2012年第3期28卷 225-234页

作者： PIAO YONG-JIE JIN HAI-LAN PIAO GUANG-RI Department of Mathematics College of Science Yanbian Universify Yanji Jilin 133002

The concept of finitely continuous topological space is introduced and the basic properties of the space are given. Several continuous selection theorems and fixed point theorems for Ф-maps are established, and as applications of the above fixed point theorems, some section problems are discussed. The results generalize and improve many corresponding conclusions.

关键词： fc-space fc-subset Ф-map continuous selection fixed point section problem

KKM Type Theorems and Coincidence Theorems in Topological spaces

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Journal of Mathematical Research and Exposition 2008年第2期28卷 403-412页

作者： ZHENG Lian DING Xie Ping Department of Mathematics Yangtze Normal University Chongqing 408100 China Department of Mathematics Sichuan Normal University Sichuan 610066 China

A class of finitely continuous topological spaces(in short,fc-spaces)is introduced. Some new KKM type theorems and coincidence theorems involving admissible set-valued map- pings and the set-valued mapping with compactly local intersection property are proved in fc- *** applications,some new fixed point theorems are obtained in *** theorems improve and generalize many known results in recent literature.

关键词： fc-space KKM type theorem coincidence theorem admissible set-valued map compactly local intersection property