THE MODIFIED MANN ITERATION METHODS FOR AN ASYMPTOTICALLY STRICT PSEUDO-CONTRACTIVE FAMILY IN HILBERT SPACES

被引：0

作者：

Kim, Kui-Yeon ^{[1
]}

Kim, Tae-Hwa ^{[1
]}

机构：

[1] Pukyong Natl Univ, Dept Appl Math, Pusan 608737, South Korea

来源：

JOURNAL OF NONLINEAR AND CONVEX ANALYSIS | 2011年 / 12卷 / 03期

关键词：

Asymptotically strict pseudo-contractive family; modified Mann's iteration method; weak (strong) convergence; parallel algorithm; cyclic algorithm; STRONG-CONVERGENCE THEOREMS; FIXED-POINTS; NONEXPANSIVE-MAPPINGS; FINITE FAMILY; APPROXIMATION; CONSTRUCTION; WEAK;

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 propose a modified Mann's iteration method for an asymptotically strict pseudo-contractive family of self-mappings defined on a closed convex subset in a Hilbert space. Next we study the weak and strong convergence of modified Mann's iteration method for such an asymptotically strict pseudo-contractive family. And some applications for the parallel algorithm and the cyclic algorithm relating to our main results are added, which extend and improve the corresponding ones due to Lopez Acedo and Xu [Nonlinear Analysis TMA, 67 (2007), 2258-2271] for a finite family of strict pseudo-contractions.

引用

页码：577 / 597

页数：21

共 29 条

[1] CONSTRUCTION OF FIXED POINTS OF NONLINEAR MAPPINGS IN HILBERT SPACE
BROWDER, FE
PETRYSHY.WV
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1967, 20 (02) : 197 - &
[2] On the convergence of implicit iteration process with error for a finite family of asymptotically nonexpansive mappings
Chang, SS
Tan, KK
Lee, HWJ
Chan, CK
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 313 (01) : 273 - 283
[3] EXAMPLE CONCERNING FIXED-POINTS
GENEL, A
LINDENSTRAUSS, J
[J]. ISRAEL JOURNAL OF MATHEMATICS, 1975, 22 (01) : 81 - 92
[4] FIXED-POINT THEOREM FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS
GOEBEL, K
KIRK, WA
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 35 (01) : 171 - &
[5] Convergence of the modified Mann's iteration method for asymptotically strict pseudo-contractions
Kim, Tae-Hwa
Xu, Hong-Kun
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 68 (09) : 2828 - 2836
[6] Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups
Kim, TH
Xu, HK
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2006, 64 (05) : 1140 - 1152
[7] Strong convergence of modified Mann iterations
Kim, TH
Xu, HK
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 61 (1-2) : 51 - 60
[8] FIXED-POINT THEOREMS FOR ASYMPTOTICALLY NONEXPANSIVE-MAPPINGS
LIM, TC
XU, HK
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1994, 22 (11) : 1345 - 1355
[9] LIONS PL, 1977, CR ACAD SCI A MATH, V284, P1357
[10] Liu QH, 1996, NONLINEAR ANAL-THEOR, V26, P1835

← 1 2 3 →