文献类型：期刊文献

英文题名：THE NONLINEAR ERGODIC THEOREM FOR ASYMPTOTICALLY NONEXPANSIVE-MAPPINGS IN BANACH-SPACES

作者：TAN, KK; XU, HK

机构：[1]E CHINA UNIV CHEM TECHNOL,DEPT MATH,SHANGHAI 200237,PEOPLES R CHINA

年份：1992

卷号：114

期号：2

起止页码：399

外文期刊名：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

收录：;WOS:【SCI-EXPANDED(收录号:WOS:A1992HB93300015)】；

语种：英文

外文关键词：ASYMPTOTICALLY NONEXPANSIVE MAPPING; NONLINEAR ERGODIC THEOREM; FIXED POINT

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, ....