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

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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-ϕ-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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