WEAK AND STRONG CONVERGENCE THEOREMS FOR COMMUTATIVE FAMILIES OF POSITIVELY HOMOGENEOUS NONEXPANSIVE MAPPINGS IN BANACH SPACES

被引：0

作者：

Takahashi, Wataru ^{[1
,2
]}

Wong, Ngai-Ching ^{[1
,3
]}

Yao, Jen-Chih ^{[3
,4
]}

机构：

[1] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 80424, Taiwan

[2] Tokyo Inst Technol, Dept Math & Comp Sci, Tokyo 1528552, Japan

[3] Kaohsiung Med Univ, Ctr Fundamental Sci, Kaohsiung 80702, Taiwan

[4] King Abdulaziz Univ, Dept Math, Jeddah 21589, Saudi Arabia

来源：

JOURNAL OF NONLINEAR AND CONVEX ANALYSIS | 2014年 / 15卷 / 03期

基金：

日本学术振兴会;

关键词：

Banach space; nonexpansive mapping; fixed point; generalized nonexpansive mapping; hybrid method; Mann's iteration; MAXIMAL MONOTONE-OPERATORS; FIXED-POINT THEOREMS; VISCOSITY APPROXIMATION METHODS; NONLINEAR ERGODIC-THEOREMS; PROXIMAL-TYPE ALGORITHM; ACCRETIVE-OPERATORS; RESOLVENTS; RETRACTIONS; SEMIGROUPS; EXISTENCE;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we first prove a weak convergence theorem by Mann's iteration for a commutative family of positively homogeneous nonexpansive mappings in a Banach space. Next, using the shrinking projection method defined by Takahashi, Takeuchi and Kubota, we prove a strong convergence theorem for such a family of the mappings. These results are new even if the mappings are linear and contractive.

引用

页码：557 / 572

页数：16

共 46 条

[1] Alber Y. I., 1994, PANAMERICAN MATH J, V4, P39
[2] Alber YI, 1996, LECT NOTES PURE APPL, P15
[3] SEMICONTRACTIVE AND SEMIACCRETIVE NONLINEAR MAPPINGS IN BANACH SPACES
BROWDER, FE
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1968, 74 (04) : 660 - &
[4] 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 - &
[5] ON THE CONVEX APPROXIMATION PROPERTY AND THE ASYMPTOTIC-BEHAVIOR OF NON-LINEAR CONTRACTIONS IN BANACH-SPACES
BRUCK, RE
[J]. ISRAEL JOURNAL OF MATHEMATICS, 1981, 38 (04) : 304 - 314
[6] Day M. M., 1957, ILLINOIS J MATH, V1, P509
[7] Ibaraki T., 2003, Abstract and Applied Analysis, V2003, P621, DOI 10.1155/S1085337503207065
[8] Ibaraki T, 2007, ADV MATH ECON, V10, P51, DOI 10.1007/978-4-431-72761-3_3
[9] A new projection and convergence theorems for the projections in Banach spaces
Ibaraki, Takanori
Takahashi, Wataru
[J]. JOURNAL OF APPROXIMATION THEORY, 2007, 149 (01) : 1 - 14
[10] Ibaraki T, 2010, CONTEMP MATH, V513, P169

← 1 2 3 4 5 →