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Vietnam Journal of Mathematics 40:2&3(2012) 319-330

 

An Iteration Method for Finding the Unique Solution of a

Variational Inequality Problem Constrained by the Intersection of the Sets

of Fixed Points of a Countable Family of Nonexpansive Mappings

in Hilbert Spaces

Lai-Jiu Lin and Chih-Sheng Chuang

Department of Mathematics, National Changhua University of Education,

Changhua, 50058, Taiwan

Dedicated to Professor Phan Quoc Khanh on the occasion of his 65th birthday

Received October 14, 2011

Revised January 18, 2012

Abstract. In this paper, we consider an iteration process which converges strongly to a common fixed point of a countable family of nonexpansive mappings, and it is the unique solution of a variational inequality constrained by this set of common fixed points. Note that our results generalize the corresponding results by Ceng et al. (Comput. Math. Appl. 61 (2011), 2447-2455).

2000 Mathematics Subject Classification. 47H10, 47H05, 47H17.

Keywords. Variational inequality, common fixed point, nonexpansive mapping.

 

 

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