THE NONLINEAR ERGODIC THEOREM FOR ASYMPTOTICALLY NONEXPANSIVE-MAPPINGS IN BANACH-SPACES

被引：72
|
作者：
TAN, KK [1 ]
XU, HK [1 ]
机构：
[1] E CHINA UNIV CHEM TECHNOL,DEPT MATH,SHANGHAI 200237,PEOPLES R CHINA
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1992年 / 114卷 / 02期
关键词：
ASYMPTOTICALLY NONEXPANSIVE MAPPING; NONLINEAR ERGODIC THEOREM; FIXED POINT;
D O I：
10.2307/2159661
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let X be a uniformly convex Banach space with a Frechet differentiable norm, C a bounded closed convex subset of X, and T:C --> C an asymptotically nonexpansive mapping. It is shown that for each x in C, the sequence {T(n)x} is weakly almost-convergent to a fixed point y of T, i.e., (1/n) SIGMA(i = 0)n-1T(k + l) x --> y weakly as n tends to infinity uniformly in k = 0, 1, 2, ....
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页码：399 / 404
页数：6
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