Approximating solutions of variational inequalities for asymptotically nonexpansive mappings

被引：12

作者：

Chang, S. S. ^{[1
]}

Lee, H. W. J. ^{[2
]}

Chan, Chi Kin ^{[2
]}

Kim, J. K. ^{[3
]}

机构：

[1] Yibin Univ, Dept Math, Yibin 644007, Sichuan, Peoples R China

[2] Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China

[3] Kyungnam Univ, Dept Math, Masan 631701, South Korea

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2009年 / 212卷 / 01期

关键词：

Asymptotically nonexpansive mappings; Viscosity approximation; Fixed point; Uniform normal structure; Uniformly Gateaux differentiable norm; Normalized duality mapping; FIXED-POINTS; STRONG-CONVERGENCE;

D O I：

10.1016/j.amc.2009.01.078

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

By using viscosity approximation methods for asymptotically nonexpansive mappings in Banach spaces, some sufficient and necessary conditions for a new type of iterative sequences to converging to a fixed point which is also the unique solution of some variational inequalities are obtained. The results presented in the paper extend and improve some recent results in [C. E. Chidume, Jinlu Li, A. Udomene, Convergence of paths and approximation of fixed points of asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 138 (2) (2005) 473-480; N. Shahzad, A. Udomene, Fixed point solutions of variational inequalities for asymptotically nonexpansive mappings in Banach spaces, Nonlinear Anal. 64 (2006) 558-567; T. C. Lim, H. K. Xu, Fixed point theories for asymptotically nonexpansive mappings, Nonlinear Anal. TMA, 22 (1994) 1345-1355; H. K. Xu, Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl., 298 (2004) 279-291]. (c) 2009 Elsevier Inc. All rights reserved.

引用

页码：51 / 59

页数：9

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