摘要
讨论了凸度量空间上不动点的存在和最佳逼近问题.主要得到以下结论:设(X,d)是一个凸度量空间,F是X的非空闭子集,T:F→X是一个连续映射且T(F)包含于X的一个紧子集D中,则T有不动点当且仅当对每一个ε>0,T具有ε-不动点;设(X,d)是一个完备的一致凸度量空间,M是X的一个闭凸集,如果对每一个x∈X,PM(x)是单点集,那么最近点投影P:X→M是连续的;设(X,d)是严格凸度量空间,MX是非空闭集,且是T-正则的,如果T是紧自映射且u∈X使d(T(x),u)≤d(x,u),x∈M,那么M中每一个u的最佳逼近点都是T的不动点.
The existence of fixed point and the best approximation problem of convex metric spaces are researched. It is obtained as follow ： Let F be a closed subset of a convex metric spaces X. Let T： F → F be a continuous map and T（F） a subset of a compact subset D of X, then T has a fixed point if and only if T has a ε -fixed point for each ε 〉 0. Let M be a closed convex subset of a uniformly convex complete metric space X. If PM （x） is singleton for each x ∈ X , then the nearest point projection P ：X→M is continuous. Let M be a nonempty closed and T-regularsubset of a strictly convex metric space X, where T is a compact self mapping and u be a point in X. Suppose that d（T（x） ,u） ≤ d（u,x） for all x in M. Then each x in M, which is best approximation to u, is a fixed point of T.
出处
《福建师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2014年第4期9-14,共6页
Journal of Fujian Normal University：Natural Science Edition
关键词
非扩张映射
拟非扩张映射
不动点
最佳逼近
凸度量空间
nonexpansive map
quasi nonexpansive map
fixed point
best approximation
convex metric space
