广义凸空间上的重叠定理、 相交定理和极大极小定理

J4 ›› 2010, Vol. 48 ›› Issue (1): 9-14.

广义凸空间上的重叠定理、相交定理和极大极小定理

朴勇杰, 沈京虎

延边大学数学系, 吉林延吉 133002

收稿日期:2009-03-08 出版日期:2010-01-26 发布日期:2010-01-27
通讯作者: 朴勇杰 E-mail:pyj6216@hotmail.com

Coincidence Theorems, Intersection Theorems and MinimaxInequality Theorems on Generalized Convex Spaces

PIAO Yongjie, SHEN Jinghu

Department of Mathematics, Yanbian University, Yanji 133002, Jilin Province, China

Received:2009-03-08 Online:2010-01-26 Published:2010-01-27
Contact: PIAO Yongjie E-mail:pyj6216@hotmail.com

摘要/Abstract

摘要：

利用已知的KKM型定理得到两个新的重叠定理, 并作为上述结果的应用, 给出了广义凸空间上的相交定理、不等式族解的存在定理和极大极小不等式定理.

关键词: G-凸空间, KKM映射, Γ-凸子集, Γ-拟凸, Γ-拟凹

Abstract:

Based on the well known KKM type theorem, two new Ky Fan type coincidence theorems were obtained, and then as the application of the above results, the intersection theorem, the existence theorems of solution for a family of inequalities and the theorems of minimax inequalities were respectively given on generalized convex spaces.

Key words: G-onvex space, KKM map, Γ-onvex subset, Γ-uasiconvex, Γ-uasiconcave

中图分类号:

O189.1

朴勇杰, 沈京虎. 广义凸空间上的重叠定理、相交定理和极大极小定理[J]. J4, 2010, 48(1): 9-14.

PIAO Yong-Jie, CHEN Jing-Hu. Coincidence Theorems, Intersection Theorems and MinimaxInequality Theorems on Generalized Convex Spaces[J]. J4, 2010, 48(1): 9-14.

[1]	朴勇杰, 石仁淑, 崔海兰. 抽象凸空间上类K的性质及聚合不动点定理[J]. J4, 2012, 50(03): 381-.
[2]	金光植, 朴勇杰. 非紧一般拓扑空间上的不动点定理[J]. J4, 2009, 47(03): 425-430.
[3]	朴勇杰, 尹哲. FC-空间上KKM定理的另一种形式及其对重合点的应用[J]. J4, 2008, 46(06): 1025-1030.
[4]	朴勇杰, 尹哲. 一般凸空间上相交定理的另一种形式及其对变分不等式的应用[J]. J4, 2008, 46(03): 438-442.