## Abstract and Applied Analysis

- Abstr. Appl. Anal.
- Volume 2014, Special Issue (2014), Article ID 965737, 12 pages.

### Strong Convergence Theorems for Mixed Equilibrium Problem and Asymptotically $I$-Nonexpansive Mapping in Banach Spaces

Bin-Chao Deng, Tong Chen, and Yi-Lin Yin

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#### Abstract

This paper aims to use a hybrid algorithm for finding a common element of a fixed point problem for a finite family of asymptotically nonexpansive mappings and the set solutions of mixed equilibrium problem in uniformly smooth and uniformly convex Banach space. Then, we prove some strong convergence theorems of the proposed hybrid algorithm to a common element of the above two sets under some suitable conditions.

#### Article information

**Source**

Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 965737, 12 pages.

**Dates**

First available in Project Euclid: 27 February 2015

**Permanent link to this document**

https://projecteuclid.org/euclid.aaa/1425048201

**Digital Object Identifier**

doi:10.1155/2014/965737

**Mathematical Reviews number (MathSciNet)**

MR3275756

**Zentralblatt MATH identifier**

07023415

#### Citation

Deng, Bin-Chao; Chen, Tong; Yin, Yi-Lin. Strong Convergence Theorems for Mixed Equilibrium Problem and Asymptotically $I$ -Nonexpansive Mapping in Banach Spaces. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 965737, 12 pages. doi:10.1155/2014/965737. https://projecteuclid.org/euclid.aaa/1425048201

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