ON THE WEAK CONVERGENCE THEOREM FOR NONEXPANSIVE SEMIGROUPS IN BANACH SPACES

被引：0
|
作者：
Yao, Rongjie [1 ]
Yang, Liping [1 ]
机构：
[1] Guangdong Univ Technol, Sch Appl Math, Guangzhou 510520, Guangdong, Peoples R China
来源：
ANNALS OF FUNCTIONAL ANALYSIS | 2017年 / 8卷 / 03期
基金：
中国国家自然科学基金;
关键词：
nonexpansive semigroups; fixed point; implicit iteration scheme; uniformly convex Banach spaces; FINITE FAMILIES;
D O I：
10.1215/20088752-0000018X
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Assume that K is a closed convex subset of a uniformly convex Banach space E, and assume that {T(s)}(s>0) is a nonexpansive semigroup on K. By using the following implicit iteration sequence {x(n)} defined by x(n) - (1 - alpha(n))x(n-1) + alpha(n) . 1/l(n) integral(tn)(0) T(s)x(n) ds, for all n >= 1, the main purpose of this paper is to establish a weak convergence theorem for the nonexpansive semigroup {T(s)}(s>0) in uniformly convex Banach spaces without the Opial property. Our results are different from some recently announced results.
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页码：341 / 349
页数：9
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