文献类型：期刊文献

英文题名：FIXED-POINT ITERATION PROCESSES FOR ASYMPTOTICALLY NONEXPANSIVE-MAPPINGS

作者：TAN, KK; XU, HK

机构：[1]E CHINA UNIV SCI & TECHNOL,INST APPL MATH,SHANGHAI 200237,PEOPLES R CHINA

年份：1994

卷号：122

期号：3

起止页码：733

外文期刊名：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

收录：;WOS:【SCI-EXPANDED(收录号:WOS:A1994PR99300012)】；

语种：英文

外文关键词：FIXED POINT; ASYMPTOTICALLY NONEXPANSIVE MAPPING; FIXED POINT ITERATION PROCESS; UNIFORMLY CONVEX BANACH SPACE; FRECHET DIFFERENTIABLE NORM; OPIALS CONDITION

摘要：Let X be a uniformly convex Banach space which satisfies Opial's condition or has a Frechet differentiable norm, C a bounded closed convex subset of X,and T: C --> C an asymptotically nonexpansive mapping. It is then shown that the modified Mann and Ishikawa iteration processes defined by x(n+1) = t(n) T(n)x(n)+(1-t(n))x(n) and x(n+1) = t(n)T(n)(s(n)T(n)x(n)+(1-s(n))x(n))+(1-t(n))x(n), respectively, converge weakly to a fixed point of T.