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

Minjiang Chen | Zendy; Jianmin Song | Zendy; Shenghua Wang | Zendy

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

Author(s) -

Minjiang Chen,

Jianmin Song,

Shenghua Wang

Publication year - 2014

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2014/193749

Subject(s) - banach space , monotone polygon , convergence (economics) , fixed point , mathematics , set (abstract data type) , iterative method , algorithm , computer science , discrete mathematics , mathematical analysis , geometry , economics , programming language , economic growth

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

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