A New Hybrid Iterative Scheme for Countable Families of Relatively Quasi-Nonexpansive Mappings and System of Equilibrium Problems

A New Hybrid Iterative Scheme for Countable Families of Relatively Quasi-Nonexpansive Mappings and System of Equilibrium Problems

We construct a new iterative scheme by hybrid methods and prove strong convergence theorem for approximation of a common fixed point of two countable families of closed relatively quasi-nonexpansive mappings which is also a solution to a system of equilibrium problems in a uniformly smooth and stric...

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Main Author: Yekini Shehu
Format: Article
Language:English
Published: Hindawi Limited 2011-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2011/131890
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spelling doaj-1a6da89267c44daf9ec5888775d411d02020-11-24T21:35:52ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252011-01-01201110.1155/2011/131890131890A New Hybrid Iterative Scheme for Countable Families of Relatively Quasi-Nonexpansive Mappings and System of Equilibrium ProblemsYekini Shehu0Mathematics Institute, African University of Science and Technology, Abuja, NigeriaWe construct a new iterative scheme by hybrid methods and prove strong convergence theorem for approximation of a common fixed point of two countable families of closed relatively quasi-nonexpansive mappings which is also a solution to a system of equilibrium problems in a uniformly smooth and strictly convex real Banach space with Kadec-Klee property using the properties of generalized f-projection operator. Using this result, we discuss strong convergence theorem concerning variational inequality and convex minimization problems in Banach spaces. Our results extend many known recent results in the literature.http://dx.doi.org/10.1155/2011/131890
collection DOAJ
language English
format Article
sources DOAJ
author Yekini Shehu
spellingShingle Yekini Shehu
A New Hybrid Iterative Scheme for Countable Families of Relatively Quasi-Nonexpansive Mappings and System of Equilibrium Problems
International Journal of Mathematics and Mathematical Sciences
author_facet Yekini Shehu
author_sort Yekini Shehu
title A New Hybrid Iterative Scheme for Countable Families of Relatively Quasi-Nonexpansive Mappings and System of Equilibrium Problems
title_short A New Hybrid Iterative Scheme for Countable Families of Relatively Quasi-Nonexpansive Mappings and System of Equilibrium Problems
title_full A New Hybrid Iterative Scheme for Countable Families of Relatively Quasi-Nonexpansive Mappings and System of Equilibrium Problems
title_fullStr A New Hybrid Iterative Scheme for Countable Families of Relatively Quasi-Nonexpansive Mappings and System of Equilibrium Problems
title_full_unstemmed A New Hybrid Iterative Scheme for Countable Families of Relatively Quasi-Nonexpansive Mappings and System of Equilibrium Problems
title_sort new hybrid iterative scheme for countable families of relatively quasi-nonexpansive mappings and system of equilibrium problems
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2011-01-01
description We construct a new iterative scheme by hybrid methods and prove strong convergence theorem for approximation of a common fixed point of two countable families of closed relatively quasi-nonexpansive mappings which is also a solution to a system of equilibrium problems in a uniformly smooth and strictly convex real Banach space with Kadec-Klee property using the properties of generalized f-projection operator. Using this result, we discuss strong convergence theorem concerning variational inequality and convex minimization problems in Banach spaces. Our results extend many known recent results in the literature.
url http://dx.doi.org/10.1155/2011/131890
work_keys_str_mv AT yekinishehu anewhybriditerativeschemeforcountablefamiliesofrelativelyquasinonexpansivemappingsandsystemofequilibriumproblems
AT yekinishehu newhybriditerativeschemeforcountablefamiliesofrelativelyquasinonexpansivemappingsandsystemofequilibriumproblems
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