## Abstract and Applied Analysis

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

#### 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 891232, 25 pages.

Dates
First available in Project Euclid: 27 February 2014

https://projecteuclid.org/euclid.aaa/1393511775

Digital Object Identifier
doi:10.1155/2013/891232

Mathematical Reviews number (MathSciNet)
MR3035305

Zentralblatt MATH identifier
1272.49061

#### Citation

Ceng, L. C.; Petruşel, A.; Yao, J. C. Relaxed Extragradient Methods with Regularization for General System of Variational Inequalities with Constraints of Split Feasibility and Fixed Point Problems. Abstr. Appl. Anal. 2013 (2013), Article ID 891232, 25 pages. doi:10.1155/2013/891232. https://projecteuclid.org/euclid.aaa/1393511775

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