An approximation method for common fixed points of a finite family of asymptotic pointwise nonexpansive mappings

被引：0

作者：

Nanjaras, Bancha ^{[1
]}

Panyanak, Bancha ^{[1
,2
]}

机构：

[1] Chaing Mai Univ, Fac Sci, Dept Math, Chiang Mai 50200, Thailand

[2] CHE, Ctr Excellence Math, Bangkok 10400, Thailand

来源：

FIXED POINT THEORY AND APPLICATIONS | 2012年

关键词：

common fixed point; asymptotic pointwise nonexpansive mapping; weak convergence; strong convergence; Banach space; CAT(0) space; IMPLICIT ITERATION PROCESS; STRONG-CONVERGENCE; THEOREM; SEMIGROUPS; PROPERTY; SPACES;

D O I：

10.1186/1687-1812-2012-108

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we consider an iterative scheme to approximate a common fixed point for a finite family of asymptotic pointwise nonexpansive mappings. We obtain weak and strong convergence theorems of the proposed iteration in uniformly convex Banach spaces. The related results for complete CAT(0) spaces are also included. MSC: 47H09, 47H10.

引用

页码：1 / 13

页数：13

共 41 条

[1] [Anonymous], 1999, METRIC SPACES NONPOS
[2] NONEXPANSIVE NONLINEAR OPERATORS IN A BANACH SPACE
BROWDER, FE
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1965, 54 (04) : 1041 - &
[3] Brown KS, 1989, Buildings
[4] Bruck R., 1993, Colloquium Mathematicum, V65, P169, DOI [10.4064/cm-65-2-169-179, DOI 10.4064/CM-65-2-169-179]
[5] An example on the Mann iteration method for Lipschitz pseudocontractions
Chidume, CE
Mutangadura, SA
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 129 (08) : 2359 - 2363
[6] Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings
Chidume, CE
Shahzad, N
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 62 (06) : 1149 - 1156
[7] Fixed points of uniformly lipschitzian mappings
Dhompongsa, S.
Kirk, W. A.
Sims, Brailey
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2006, 65 (04) : 762 - 772
[8] On Δ-convergence theorems in CAT(0) spaces
Dhompongsa, S.
Panyanak, B.
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 56 (10) : 2572 - 2579
[9] THEOREM ON MEAN-VALUE ITERATIONS
FRANKS, RL
MARZEC, RP
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1971, 30 (02) : 324 - &
[10] Convergence of Ishikawa iterates of quasi-nonexpansive mappings
Ghosh, MK
Debnath, L
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1997, 207 (01) : 96 - 103

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