## 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

#### 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

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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