Strong Convergence Theorems for Countable Families of Uniformly Quasi-ϕ-Asymptotically Nonexpansive Mappings and a System of Generalized Mixed Equilibrium Problems | Zendy

Siwaporn Saewan | Zendy; Poom Kumam | Zendy

Open Access

Strong Convergence Theorems for Countable Families of Uniformly Quasi-ϕ-Asymptotically Nonexpansive Mappings and a System of Generalized Mixed Equilibrium Problems

Author(s) -

Siwaporn Saewan,

Poom Kumam

Publication year - 2011

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2011/701675

Subject(s) - countable set , mathematics , banach space , convergence (economics) , regular polygon , projection (relational algebra) , set (abstract data type) , fixed point , element (criminal law) , algorithm , discrete mathematics , mathematical analysis , computer science , geometry , political science , law , economics , programming language , economic growth

The purpose of this paper is to present a new hybrid block iterative scheme by the generalized f-projection method for finding a common element of the fixed point set for a countable family of uniformlyquasi-ϕ-asymptotically nonexpansive mappings and the set of solutions of the system of generalized mixedequilibrium problems in a strictly convex and uniformly smooth Banach space with the Kadec-Kleeproperty. Furthermore, we prove that our new iterative scheme converges strongly to a common elementof the aforementioned sets. The results presented in this paper improve and extend important recentresults in the literature

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