VISCOSITY ITERATIVE METHODS FOR COMMON FIXED POINTS OF TWO NONEXPANSIVE MAPPINGS WITHOUT COMMUTATIVITY ASSUMPTION IN HILBERT SPACES

doi:10.1016/S0252-9602(11)60271-3

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (2): 716-726.doi: 10.1016/S0252-9602(11)60271-3

VISCOSITY ITERATIVE METHODS FOR COMMON FIXED POINTS OF TWO NONEXPANSIVE MAPPINGS WITHOUT COMMUTATIVITY ASSUMPTION IN HILBERT SPACES

Eknarin Jankaew|Somyot Plubtieng|Anutep Tepphun

Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand.

收稿日期:2008-02-18 修回日期:2009-08-24 出版日期:2011-03-20 发布日期:2011-03-20
基金资助:
The second author would like to thank the Thailand Research Fund for financial support under Grant BRG5280016

VISCOSITY ITERATIVE METHODS FOR COMMON FIXED POINTS OF TWO NONEXPANSIVE MAPPINGS WITHOUT COMMUTATIVITY ASSUMPTION IN HILBERT SPACES

Eknarin Jankaew|Somyot Plubtieng|Anutep Tepphun

Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand.

Received:2008-02-18 Revised:2009-08-24 Online:2011-03-20 Published:2011-03-20
Supported by:
The second author would like to thank the Thailand Research Fund for financial support under Grant BRG5280016

摘要/Abstract

摘要：

In this article, we introduce a new viscosity iterative method for two nonexpansive mappings in Hilbert spaces. We also prove, without
commutativity assumption, that the iterates converge to a common fixed point of the mappings which solves some variational
inequality. The results presented extend the corresponding results of Shimizu and Takahashi [T. Shimizu, W. Takahashi, Strong
convergence to common fixed point of families of nonexpansive mappings, J. Math. Anal. Appl. 211 (1997), 71-83], and Yao and Chen[Y. Yao, R. Chen, Convergence to common fixed points of average mappings without commutativity assumption in Hilbert spaces,Nonlinear Analysis 67(2007), 1758-1763].

关键词: Viscosity iterative method, common fixed points, nonexpansive mappings, variational inequality

Abstract:

Key words: Viscosity iterative method, common fixed points, nonexpansive mappings, variational inequality

中图分类号:

41A50

Eknarin Jankaew, Somyot Plubtieng, Anutep Tepphun . VISCOSITY ITERATIVE METHODS FOR COMMON FIXED POINTS OF TWO NONEXPANSIVE MAPPINGS WITHOUT COMMUTATIVITY ASSUMPTION IN HILBERT SPACES[J]. 数学物理学报(英文版), 2011, 31(2): 716-726.

参考文献

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VISCOSITY ITERATIVE METHODS FOR COMMON FIXED POINTS OF TWO NONEXPANSIVE MAPPINGS WITHOUT COMMUTATIVITY ASSUMPTION IN HILBERT SPACES

VISCOSITY ITERATIVE METHODS FOR COMMON FIXED POINTS OF TWO NONEXPANSIVE MAPPINGS WITHOUT COMMUTATIVITY ASSUMPTION IN HILBERT SPACES

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