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Journal of Applied Mathematics
Volume 2012, Article ID 174318, 20 pages
http://dx.doi.org/10.1155/2012/174318
Research Article

General Iterative Algorithms for Hierarchical Fixed Points Approach to Variational Inequalities

Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangmod, Bangkok 10140, Thailand

Received 24 March 2012; Accepted 16 May 2012

Academic Editor: Zhenyu Huang

Copyright © 2012 Nopparat Wairojjana and Poom Kumam. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper deals with new methods for approximating a solution to the fixed point problem; find x̃F(T), where H is a Hilbert space, C is a closed convex subset of H, f is a ρ-contraction from C into H, 0<ρ<1, A is a strongly positive linear-bounded operator with coefficient γ̅>0, 0<γ<γ̅/ρ, T is a nonexpansive mapping on C, and PF(T) denotes the metric projection on the set of fixed point of T. Under a suitable different parameter, we obtain strong convergence theorems by using the projection method which solves the variational inequality (A-γf)x̃+τ(I-S)x̃,x-x̃0 for xF(T), where τ[0,). Our results generalize and improve the corresponding results of Yao et al. (2010) and some authors. Furthermore, we give an example which supports our main theorem in the last part.