## Abstract and Applied Analysis

### Composite Algorithms for Minimization over the Solutions of Equilibrium Problems and Fixed Point Problems

#### Abstract

The purpose of this paper is to solve the minimization problem of finding ${x}^{\ast\,\!}$ such that ${x}^{\ast\,\!}=\arg {\min }_{x\in \Gamma }{\Vert x\Vert }^{2}$, where $\Gamma$ stands for the intersection set of the solution set of the equilibrium problem and the fixed points set of a nonexpansive mapping. We first present two new composite algorithms (one implicit and one explicit). Further, we prove that the proposed composite algorithms converge strongly to ${x}^{\ast\,\!}$.

#### Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 763506, 19 pages.

Dates
First available in Project Euclid: 1 November 2010

https://projecteuclid.org/euclid.aaa/1288620781

Digital Object Identifier
doi:10.1155/2010/763506

Mathematical Reviews number (MathSciNet)
MR2726615

Zentralblatt MATH identifier
1203.49048

#### Citation

Yao, Yonghong; Liou, Yeong-Cheng. Composite Algorithms for Minimization over the Solutions of Equilibrium Problems and Fixed Point Problems. Abstr. Appl. Anal. 2010 (2010), Article ID 763506, 19 pages. doi:10.1155/2010/763506. https://projecteuclid.org/euclid.aaa/1288620781