Strong convergence of composite iterative schemes for zeros of m-accretive operators in Banach spaces

被引：41

作者：

Ceng, L. -C. ^{[2
]}

Khan, A. R. ^{[1
]}

Ansari, Q. H. ^{[1
,3
]}

Yao, J. -C. ^{[4
]}

机构：

[1] King Fahd Univ Petr & Minerals, Dept Math & Stat, Dhahran 31261, Saudi Arabia

[2] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

[3] Aligarh Muslim Univ, Dept Math, Aligarh, Uttar Pradesh, India

[4] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 804, Taiwan

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 70卷 / 05期

关键词：

m-accretive operator; Zero of an operator; Composite iterative scheme; Uniformly smooth; Weakly continuous duality map; FIXED-POINT THEOREMS; NONLINEAR OPERATORS; MAPPINGS; APPROXIMATION;

D O I：

10.1016/j.na.2008.02.083

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce a new composite iterative scheme to approximate a zero of an in-accretive operator A defined on uniform smooth Banach spaces and a reflexive Banach space having a weakly continuous duality map. It is shown that the iterative process in each case converges strongly to a zero of A. The results presented in this paper substantially improve and extend the results due to Ceng et al. [L.C. Ceng, H.K. Xu, J.C. Yao, Strong convergence of a hybrid viscosity approximation method with perturbed mappings for nonexpansive and accretive operators, Taiwanese J. Math. (in press)], Kim and Xu [T.H. Kim, H.K. Xu, Strong convergence of modified Mann iterations, Nonlinear Anal. 61 (2005) 51-60] and Xu [H.K. Xu, Strong convergence of an iterative method for nonexpansive and accretive operators, J. Math. Anal. Appl. 314 (2006) 631-643]. Our work provides a new approach for the construction of a zero of in-accretive operators. (C) 2009 Published by Elsevier Ltd

引用

页码：1830 / 1840

页数：11

共 15 条

[1] Barbu V, 1976, Nonlinear Semigroups and Differential Equations in Banach Spaces, Editura Academiei Republicii Socialiste Romania
[2] FIXED-POINT THEOREMS FOR NONCOMPACT MAPPINGS IN HILBERT SPACE
BROWDER, FE
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1965, 53 (06) : 1272 - &
[3] CONVERGENCE THEOREMS FOR SEQUENCES OF NONLINEAR OPERATORS IN BANACH SPACES
BROWDER, FE
[J]. MATHEMATISCHE ZEITSCHRIFT, 1967, 100 (03) : 201 - &
[4] NONEXPANSIVE PROJECTIONS ON SUBSETS OF BANACH SPACES
BRUCK, RE
[J]. PACIFIC JOURNAL OF MATHEMATICS, 1973, 47 (02) : 341 - 355
[5] CENG LC, NUMER FUNCT IN PRESS
[6] Strong convergence of a hybrid viscosity approximation method with perturbed mappings for nonexpansive and accretive operators
Ceng, Lu-Chuan
Xu, Hong-Kun
[J]. TAIWANESE JOURNAL OF MATHEMATICS, 2007, 11 (03): : 661 - 682
[7] Geobel K., 1984, UNIFORM CONVEXITY HY
[8] Strong convergence of modified Mann iterations
Kim, TH
Xu, HK
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 61 (1-2) : 51 - 60
[9] FIXED-POINT THEOREMS FOR ASYMPTOTICALLY NONEXPANSIVE-MAPPINGS
LIM, TC
XU, HK
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1994, 22 (11) : 1345 - 1355
[10] Approximation of a zero point of accretive operator in Banach spaces
Qin, Xiaolong
Su, Yongfu
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 329 (01) : 415 - 424

← 1 2 →