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

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--asymptotically nonexpansive mappings, the set of the variational inequality for an α-inverse-strongly monotone oper...

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Bibliographic Details
Published in:Fixed point theory and algorithms for sciences and engineering Vol. 2011; no. 1; pp. 1 - 24
Main Authors: Saewan, Siwaporn, Kumam, Poom
Format: Journal Article
Language:English
Published: New York Springer Nature B.V 01.12.2011
Subjects:
Banach space
Blocking
Convergence
Inequalities
Iterative algorithms
Mapping
Operators
Theorems
ISSN:1687-1820, 2730-5422, 1687-1812
Online Access:Get full text
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Summary: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--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.[PUBLICATION ABSTRACT]
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ISSN:1687-1820
2730-5422
1687-1812
DOI:10.1186/1687-1812-2011-35