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

Abstract

Abstract:

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].

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

CLC Number:

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].Acta mathematica scientia,Series B, 2011, 31(2): 716-726.

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