Fixed Point Theory and Applications
Volume 2011 (2011), Article ID 180534, 8 pages
doi:10.1155/2011/180534
Research Article

A Hybrid Method for Monotone Variational Inequalities Involving Pseudocontractions

Yonghong Yao,1 Giuseppe Marino,2 and Yeong-Cheng Liou3

1Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China
2Dipartimento di Matematica, Universitá della Calabria, 87036 Arcavacata di Rende (CS), Italy
3Department of Information Management, Cheng Shiu University, Kaohsiung 833, Taiwan

Received 25 November 2010; Accepted 24 January 2011

Academic Editor: Marlène Frigon

Copyright © 2011 Yonghong Yao et al. 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

We use strongly pseudocontraction to regularize the following ill-posed monotone variational inequality: finding a point 𝑥 ∗ with the property 𝑥 ∗ ∈ F i x ( 𝑇 ) such that ⟨ ( 𝐼 − 𝑆 ) 𝑥 ∗ , 𝑥 − 𝑥 ∗ ⟩ ≥ 0 , 𝑥 ∈ F i x ( 𝑇 ) where 𝑆 , 𝑇 are two pseudocontractive self-mappings of a closed convex subset 𝐶 of a Hilbert space with the set of fixed points F i x ( 𝑇 ) ≠ ∅ . Assume the solution set Ω of (VI) is nonempty. In this paper, we introduce one implicit scheme which can be used to find an element 𝑥 ∗ ∈ Ω . Our results improve and extend a recent result of (Lu et al. 2009).