A New Hybrid Method for Equilibrium Problems, Variational Inequality Problems, Fixed Point Problems, and Zero of Maximal Monotone Operators

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, the set of solutions of the generalized mixed equilibrium problem, and zeros of maxima...

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Main Author: Yaqin Wang
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/712651
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author Yaqin Wang
author_facet Yaqin Wang
author_sort Yaqin Wang
collection DOAJ
description 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, the set of solutions of the generalized mixed equilibrium problem, and zeros of maximal monotone operators in a 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 obtained in this paper improve and extend the result of Zeng et al. (2010) and many others.
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spelling doaj-art-91a7209cd74e49a68849340f4041f2692025-08-20T02:10:09ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/712651712651A New Hybrid Method for Equilibrium Problems, Variational Inequality Problems, Fixed Point Problems, and Zero of Maximal Monotone OperatorsYaqin Wang0Mathematical College, Sichuan University, Chengdu, Sichuan 610064, ChinaWe 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, the set of solutions of the generalized mixed equilibrium problem, and zeros of maximal monotone operators in a 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 obtained in this paper improve and extend the result of Zeng et al. (2010) and many others.http://dx.doi.org/10.1155/2012/712651
spellingShingle Yaqin Wang
A New Hybrid Method for Equilibrium Problems, Variational Inequality Problems, Fixed Point Problems, and Zero of Maximal Monotone Operators
Journal of Applied Mathematics
title A New Hybrid Method for Equilibrium Problems, Variational Inequality Problems, Fixed Point Problems, and Zero of Maximal Monotone Operators
title_full A New Hybrid Method for Equilibrium Problems, Variational Inequality Problems, Fixed Point Problems, and Zero of Maximal Monotone Operators
title_fullStr A New Hybrid Method for Equilibrium Problems, Variational Inequality Problems, Fixed Point Problems, and Zero of Maximal Monotone Operators
title_full_unstemmed A New Hybrid Method for Equilibrium Problems, Variational Inequality Problems, Fixed Point Problems, and Zero of Maximal Monotone Operators
title_short A New Hybrid Method for Equilibrium Problems, Variational Inequality Problems, Fixed Point Problems, and Zero of Maximal Monotone Operators
title_sort new hybrid method for equilibrium problems variational inequality problems fixed point problems and zero of maximal monotone operators
url http://dx.doi.org/10.1155/2012/712651
work_keys_str_mv AT yaqinwang anewhybridmethodforequilibriumproblemsvariationalinequalityproblemsfixedpointproblemsandzeroofmaximalmonotoneoperators
AT yaqinwang newhybridmethodforequilibriumproblemsvariationalinequalityproblemsfixedpointproblemsandzeroofmaximalmonotoneoperators