Approximation of fixed points for amenable semigroups of nonexpansive mappings in Banach spaces

被引：55
作者：
Lau, Anthony To-Ming
Miyake, Hiromichi
Takahashi, Wataru
机构：
[1] Tokyo Inst Technol, Grad Sch Informat Sci & Engn, Dept Math & Comp Sci, Meguro Ku, Tokyo 1528552, Japan
[2] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2007年 / 67卷 / 04期
基金：
加拿大自然科学与工程研究理事会;
关键词：
D O I：
10.1016/j.na.2006.07.008
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The purpose of this paper is to study iterative schemes of Browder and Halpern types for a semigroup of nonexpansive mappings on a compact convex subset of a smooth (and strictly convex) Banach space with respect to a sequence of strongly asymptotic invariant means defined on an appropriate space of bounded real valued functions of the semigroup. Various applications to the additive semigroup of nonnegative real numbers and commuting pairs of nonexpansive mappings are also presented. (c) 2006 Elsevier Ltd. All rights reserved.
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页码：1211 / 1225
页数：15
相关论文
共 31 条
[1]  
Atsushiba S., 2000, Math. Jpn., V52, P183
[2]  
BAILLON JB, 1975, CR ACAD SCI A MATH, V280, P1511
[3]   NONLINEAR ERGODIC THEOREMS [J].
BREZIS, H ;
BROWDER, FE .
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1976, 82 (06) :959-961
[4]   REMARKS ON NONLINEAR ERGODIC THEORY [J].
BREZIS, H ;
BROWDER, FE .
ADVANCES IN MATHEMATICS, 1977, 25 (02) :165-177
[5]  
BROWDER FE, 1967, ARCH RATION MECH AN, V24, P82
[6]   ON THE CONVEX APPROXIMATION PROPERTY AND THE ASYMPTOTIC-BEHAVIOR OF NON-LINEAR CONTRACTIONS IN BANACH-SPACES [J].
BRUCK, RE .
ISRAEL JOURNAL OF MATHEMATICS, 1981, 38 (04) :304-314
[7]   SIMPLE PROOF OF THE MEAN ERGODIC THEOREM FOR NON-LINEAR CONTRACTIONS IN BANACH-SPACES [J].
BRUCK, RE .
ISRAEL JOURNAL OF MATHEMATICS, 1979, 32 (2-3) :107-116
[8]  
Day M. M., 1957, Illinois J. Math., V1, P509
[9]   FIXED POINTS OF NONEXPANDING MAPS [J].
HALPERN, B .
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1967, 73 (06) :957-&
[10]   NONEXPANSIVE RETRACTIONS AND NONLINEAR ERGODIC-THEOREMS IN BANACH-SPACES [J].
HIRANO, N ;
KIDO, K ;
TAKAHASHI, W .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1988, 12 (11) :1269-1281
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