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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Vydáno v:Fixed point theory and algorithms for sciences and engineering Ročník 2011; číslo 1; s. 1 - 24
Hlavní autoři: Saewan, Siwaporn, Kumam, Poom
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer Nature B.V 01.12.2011
Témata:
Banach space
Blocking
Convergence
Inequalities
Iterative algorithms
Mapping
Operators
Theorems
ISSN:1687-1820, 2730-5422, 1687-1812
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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--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]
AbstractList 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 alpha -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.
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]
Author Saewan, Siwaporn
Kumam, Poom
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Snippet 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...
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SubjectTerms Banach space
Blocking
Convergence
Inequalities
Iterative algorithms
Mapping
Operators
Theorems
Title A new modified block iterative algorithm for uniformly quasi--asymptotically nonexpansive mappings and a system of generalized mixed equilibrium problems
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