A Hybrid Iterative Scheme for a Maximal Monotone Operator and Two Countable Families of Relatively Quasi-Nonexpansive Mappings for Generalized Mixed Equilibrium and Variational Inequality Problems

Siwaporn Saewan and Poom Kumam

Abstract and Applied Analysis, 2010, vol. 2010, 1-31

Abstract:

We introduce a new hybrid iterative scheme for finding a common element of the set of common fixed points of two countable families of relatively quasi-nonexpansive mappings, the set of the variational inequality for an α -inverse-strongly monotone operator, the set of solutions of the generalized mixed equilibrium problem and zeros of a maximal monotone operator in the framework of a real Banach space. We obtain a strong convergence theorem for the sequences generated by this process in a 2 uniformly convex and uniformly smooth Banach space. The results presented in this paper improve and extend some recent results.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:123027

DOI: 10.1155/2010/123027

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