中文核心期刊
CSCD来源期刊
中国科技核心期刊
RCCSE中国核心学术期刊
重庆交通大学学报（自然科学版）

重庆交通大学学报（自然科学版） ›› 1991, Vol. 10 ›› Issue (2): 59-62.

• • 上一篇    下一篇

抽象度量空间中的凸结构及其不动点

郑权1, 丁佐华2   

  1. 1. 武汉: 华中理工大学;
    2. 南京航空学院
  • 收稿日期:1990-02-08 出版日期:1991-04-22 发布日期:2016-11-09
  • 作者简介:郑权,男,29岁,讲师。

A Convex Structure of Abstract Metric Spaces and Its Fixed Points

Zheng Quan1, Ding Zuohua2   

  1. 1. Huazhong University of Science and Technology, Wuhan;
    2. Nanjing Aeronautical Institute, Nanjing
  • Received:1990-02-08 Online:1991-04-22 Published:2016-11-09

PDF

摘要： 本文在抽象度量空间中引入了凸结构的概念,并得到以下非扩张映象的不动点定理:定理,设(X,r)是完备的凸抽象度量空间,K⊂X是有界闭星形集,x0为星形中心,K满足r((W<sub>A(x,x0),(WA,(y,x0))≤AR(x,y),∀x,y∈K.这里WA是X的凸结构,A是r取值的半序空间中的一个映象,并满足适当的条件。又设f:K→K是(WA,x0)凸的,且存在正整数m,使得fm在{WA(x,x0);x∈f(K)}上紧及r(fx,fy)≤r(x,y),∀x,y∈K.则f在K中存在不动点。

关键词: 抽象度量空间, 凸结构, 不动点

Abstract: Our purpose is to introduce the concept of a convex structure of abstract metric spaces, by virtue of which we prove the following fixed point theorem for nonex-pansive mappings.Theorem. Let (X,r) be a complete convex abstract metric spaces. Let K⊂X be a bounded closed star shaped set, xa be its center, satisfying r((WA(x,x0),(WA,(y,x0))≤AR(x,y),∀x,y∈K.where WA is the convex structure of X, and A, which satisfies some conditions, is a mapping in a partially ordered space. Suppose further that mapping f:K-K is (WA, x0) convex, m is a positive integral number such that fm is compact on {WA(x,x0;x∈f(K)) and r(fx,fy)≤r(x,y) for x,y∈K. Then f has a fixed point in K.

Key words: abstract metric space, convex structure, fixed point