## Abstract and Applied Analysis

### Hybrid Extragradient-Like Viscosity Methods for Generalized Mixed Equilibrium Problems, Variational Inclusions, and Optimization Problems

#### Abstract

We introduce and analyze a new hybrid extragradient-like viscosity iterative algorithm for finding a common solution of a generalized mixed equilibrium problem, a finite family of variational inclusions for maximal monotone and inverse strongly monotone mappings, and a fixed point problem of infinitely many nonexpansive mappings in a real Hilbert space. Under some mild conditions, we prove the strong convergence of the sequence generated by the proposed algorithm to a common solution of these three problems which also solves an optimization problem.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 120172, 22 pages.

Dates
First available in Project Euclid: 6 October 2014

https://projecteuclid.org/euclid.aaa/1412606987

Digital Object Identifier
doi:10.1155/2014/120172

Mathematical Reviews number (MathSciNet)
MR3170388

Zentralblatt MATH identifier
07021752

#### Citation

Ceng, Lu-Chuan; Chen, Chi-Ming; Pang, Chin-Tzong. Hybrid Extragradient-Like Viscosity Methods for Generalized Mixed Equilibrium Problems, Variational Inclusions, and Optimization Problems. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 120172, 22 pages. doi:10.1155/2014/120172. https://projecteuclid.org/euclid.aaa/1412606987

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