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Fixed Point Theory and Applications
Article . 2011
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A new modified block iterative algorithm for uniformly quasi-ϕ-asymptotically nonexpansive mappings and a system of generalized mixed equilibrium problems

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2011 English Publisher:SpringerOpenJournal:Fixed Point Theory and Applications (issn: 1687-1820, Copyright policy )
Authors: Saewan Siwaporn; Kumam Poom;

A new modified block iterative algorithm for uniformly quasi-ϕ-asymptotically nonexpansive mappings and a system of generalized mixed equilibrium problems

Abstract

Abstract In this paper, we introduce a new modified block iterative algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi-ϕ-asymptotically nonexpansive mappings, the set of the variational inequality for an α-inverse-strongly monotone operator, and the set of solutions of a system of generalized mixed equilibrium problems. We obtain a strong convergence theorem for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach space. Our results extend and improve ones from several earlier works. 2000 MSC: 47H05; 47H09; 47H10.

Keywords

T57-57.97, QA299.6-433, Applied mathematics. Quantitative methods, uniformly quasi-<it>&#981;</it>-asymptotically nonexpansive mapping, a system of generalized mixed equilibrium problem, modified block iterative algorithm, variational inequality, Analysis, inverse-strongly monotone operator

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popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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