Abstract and Applied Analysis
Volume 2013 (2013), Article ID 891232, 25 pages
http://dx.doi.org/10.1155/2013/891232
Research Article

Relaxed Extragradient Methods with Regularization for General System of Variational Inequalities with Constraints of Split Feasibility and Fixed Point Problems

L. C. Ceng,1 A. Petruşel,2 and J. C. Yao3,4

1Department of Mathematics, Shanghai Normal University, and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, China
2Department of Applied Mathematics, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania
3Center for Fundamental Science, Kaohsiung Medical University, Kaohsiung 807, Taiwan
4Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung 804, Taiwan

Received 1 September 2012; Accepted 15 October 2012

Academic Editor: Julian López-Gómez

Copyright © 2013 L. C. Ceng 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 suggest and analyze relaxed extragradient iterative algorithms with regularization for finding a common element of the solution set of a general system of variational inequalities, the solution set of a split feasibility problem, and the fixed point set of a strictly pseudocontractive mapping defined on a real Hilbert space. Here the relaxed extragradient methods with regularization are based on the well-known successive approximation method, extragradient method, viscosity approximation method, regularization method, and so on. Strong convergence of the proposed algorithms under some mild conditions is established. Our results represent the supplementation, improvement, extension, and development of the corresponding results in the very recent literature.