## Abstract and Applied Analysis

- Abstr. Appl. Anal.
- Volume 2013 (2013), Article ID 107296, 13 pages.

### A New Hybrid Projection Algorithm for System of Equilibrium Problems and Variational Inequality Problems and Two Finite Families of Quasi-$\varphi $-Nonexpansive Mappings

Pongrus Phuangphoo and Poom Kumam

#### Abstract

We introduce a modified Mann’s iterative procedure by using the hybrid projection method for solving the common solution of the system of equilibrium problems for a finite family of bifunctions satisfying certain condition, the common solution of fixed point problems for two finite families of quasi-$\varphi $-nonexpansive mappings, and the common solution of variational inequality problems for a finite family of continuous monotone mappings in a uniformly smooth and strictly convex real Banach space. Then, we prove a strong convergence theorem of the iterative procedure generated by some mild conditions. Our result presented in this paper improves and generalizes some well-known results in the literature.

#### Article information

**Source**

Abstr. Appl. Anal., Volume 2013 (2013), Article ID 107296, 13 pages.

**Dates**

First available in Project Euclid: 18 April 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.aaa/1366306740

**Digital Object Identifier**

doi:10.1155/2013/107296

**Mathematical Reviews number (MathSciNet)**

MR3034906

**Zentralblatt MATH identifier**

1263.49007

#### Citation

Phuangphoo, Pongrus; Kumam, Poom. A New Hybrid Projection Algorithm for System of Equilibrium Problems and Variational Inequality Problems and Two Finite Families of Quasi- $\varphi $ -Nonexpansive Mappings. Abstr. Appl. Anal. 2013 (2013), Article ID 107296, 13 pages. doi:10.1155/2013/107296. https://projecteuclid.org/euclid.aaa/1366306740