Acta mathematica scientia, Series B >
VISCOSITY ITERATIVE METHODS FOR COMMON FIXED POINTS OF TWO NONEXPANSIVE MAPPINGS WITHOUT COMMUTATIVITY ASSUMPTION IN HILBERT SPACES
Received date: 2008-02-18
Revised date: 2009-08-24
Online published: 2011-03-20
Supported by
The second author would like to thank the Thailand Research Fund for financial support under Grant BRG5280016
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].
Eknarin Jankaew , Somyot Plubtieng , Anutep Tepphun . VISCOSITY ITERATIVE METHODS FOR COMMON FIXED POINTS OF TWO NONEXPANSIVE MAPPINGS WITHOUT COMMUTATIVITY ASSUMPTION IN HILBERT SPACES[J]. Acta mathematica scientia, Series B, 2011 , 31(2) : 716 -726 . DOI: 10.1016/S0252-9602(11)60271-3
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