抽象凸空间上类K的性质及聚合不动点定理

J4 ›› 2012, Vol. 50 ›› Issue (03): 381-.

抽象凸空间上类K的性质及聚合不动点定理

朴勇杰¹, 石仁淑¹, 崔海兰²

1. 延边大学理学院数学系, 吉林延吉 133002|2. 吉林市朝鲜族中学, 吉林吉林 132001

收稿日期:2011-08-08 出版日期:2012-05-26 发布日期:2012-05-28
通讯作者: 朴勇杰 E-mail:pyj6216@hotmail.com

Properties of Class K and Collectively Fixed PointTheorems on Abstract Convex Spaces

PIAO Yongjie¹, SHI Renshu¹, CUI Hailan²

1. Department of Mathematics, College of Science, Yanbian University, Yanji 133002, Jilin Province, China;2. Jilin Korean Middle School, Jilin 132001, Jilin Province, China

Received:2011-08-08 Online:2012-05-26 Published:2012-05-28
Contact: PIAO Yongjie E-mail:pyj6216@hotmail.com

摘要/Abstract

摘要：

给出抽象凸空间上映射类K的两个性质, 利用已知抽象凸空间上的重叠点定理讨论抽象凸空间上映射的不动点存在问题, 得到了若干新的不动点定理, 同时进一步给出了抽象凸空间族的乘积空间上映射族的聚合不动点定理.

关键词: 抽象凸空间, 映射类K,KC,KO, 聚合不动点定理, KKM映射

Abstract:

We first gave two properties of map class K on abstract convex spaces, and then used the wellknown coincidence point theorem on abstract convex spaces to discuss the existence problem of fixed points for maps on abstract convex spaces and obtained some new fixed point theorems, from which several collectively fixed point theorems were established for a family of maps on a product space of a family of abstract convex spaces.

Key words: abstract convex space, map class K,KC,KO, collectively fixed point theorem, KKM map

中图分类号:

O177.3

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-.

PIAO Yong-Jie, DAN Ren-Chu, CUI Hai-Lan. Properties of Class K and Collectively Fixed PointTheorems on Abstract Convex Spaces[J]. J4, 2012, 50(03): 381-.

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[2]	朴勇杰. 抽象凸空间上的不动点定理、匹配定理和全交定理[J]. J4, 2010, 48(06): 882-886.
[3]	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.
[4]	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.
[5]	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.