## Journal of Applied Mathematics

- J. Appl. Math.
- Volume 2014, Special Issue (2013), Article ID 193749, 10 pages.

### New Mixed Equilibrium Problems and Iterative Algorithms for Fixed Point Problems in Banach Spaces

Minjiang Chen, Jianmin Song, and Shenghua Wang

**Full-text: Open access**

#### Abstract

We first introduce a new mixed equilibrium problem with a relaxed monotone mapping in Banach spaces and prove the existence of solutions of the equilibrium problem. Then we introduce a new iterative algorithm for finding a common element of the set of solutions of the equilibrium problem and the set of fixed points of a quasi-$\varphi $-nonexpansive mapping and prove some strong convergence theorems of the iteration. Our results extend and improve the corresponding ones given by Wang et al., Takahashi and Zembayashi, and some others.

#### Article information

**Source**

J. Appl. Math., Volume 2014, Special Issue (2013), Article ID 193749, 10 pages.

**Dates**

First available in Project Euclid: 26 March 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.jam/1395855209

**Digital Object Identifier**

doi:10.1155/2014/193749

**Mathematical Reviews number (MathSciNet)**

MR3166754

#### Citation

Chen, Minjiang; Song, Jianmin; Wang, Shenghua. New Mixed Equilibrium Problems and Iterative Algorithms for Fixed Point Problems in Banach Spaces. J. Appl. Math. 2014, Special Issue (2013), Article ID 193749, 10 pages. doi:10.1155/2014/193749. https://projecteuclid.org/euclid.jam/1395855209

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Digital Object Identifier: doi:10.1007/s10483-009-0904-6

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