## Abstract and Applied Analysis

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

#### 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

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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