拓扑空间上不动点和具有上下界的变分不等式

数学物理学报 ›› 2012, Vol. 32 ›› Issue (2): 364-372.

拓扑空间上不动点和具有上下界的变分不等式

朴勇杰

延边大学理学院数学系吉林延吉 133002

收稿日期:2010-10-12 修回日期:2011-09-02 出版日期:2012-04-25 发布日期:2012-04-25
基金资助:
吉林省教育厅科研项目(吉教科合字[2011]第434号)资助

Fixed Points and Variational Inequalities |with Lower and Upper Bounds in Topological Spaces

PIAO Yong-Jie

Department of Mathematics, College of Science, Yanbian University, Jilin Yanji 133002

Received:2010-10-12 Revised:2011-09-02 Online:2012-04-25 Published:2012-04-25
Supported by:
吉林省教育厅科研项目(吉教科合字[2011]第434号)资助

摘要/Abstract

摘要：

ωω根据广义凸空间上的KKM型定理和Fan-Browder型不动点定理, 得到了没有凸和线性结构且没有紧致框架的拓扑空间上的Φ -映射和弱Φ -映射的若干个新的不动点定理. 作为应用, 在非紧致的拓扑空间上讨论了具有上下界的变分不等式解的存在性问题.

关键词: 广义凸空间, KKM映射, &omega, -连通, Φ-映射, 弱&Phi, -映射, 变分不等式

Abstract:

Based on an KKM type theorem and a Fan-Browder type fixed point theorem on generalized convex space, some new fixed point theorems for a Φ-map and a weak Φ-map defined on topological spaces without any convex and linear structure and any compact setting are obtained. As applications, some existence problems of solutions for variational inequalities with lower and upper bounds were discussed in non-compact topological spaces.

Key words: Generalized convex space, KKM map, ω-connected, Φ-map, Weak Φ-map, Variational inequality

中图分类号:

47H10

朴勇杰. 拓扑空间上不动点和具有上下界的变分不等式[J]. 数学物理学报, 2012, 32(2): 364-372.

PIAO Yong-Jie. Fixed Points and Variational Inequalities |with Lower and Upper Bounds in Topological Spaces[J]. Acta mathematica scientia,Series A, 2012, 32(2): 364-372.

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