Strong convergence of gradient projection method for generalized equilibrium problem in a Banach space

In this paper, we propose and analyze a hybrid iterative method for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of a variational inequality problem, and the set of fixed points of a relatively nonexpansive mapping in a real Banach space...

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Detalles Bibliográficos
Autores principales: Farid, Mohammad, Irfan, Syed Shakaib, Khan, Mohammad Firdosh, Khan, Suhel Ahmad
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5705783/
https://www.ncbi.nlm.nih.gov/pubmed/29213202
http://dx.doi.org/10.1186/s13660-017-1574-x
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author Farid, Mohammad
Irfan, Syed Shakaib
Khan, Mohammad Firdosh
Khan, Suhel Ahmad
author_facet Farid, Mohammad
Irfan, Syed Shakaib
Khan, Mohammad Firdosh
Khan, Suhel Ahmad
author_sort Farid, Mohammad
collection PubMed
description In this paper, we propose and analyze a hybrid iterative method for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of a variational inequality problem, and the set of fixed points of a relatively nonexpansive mapping in a real Banach space. Further, we prove the strong convergence of the sequences generated by the iterative scheme. Finally, we derive some consequences from our main result. Our work is an improvement and extension of some previously known results recently obtained by many authors.
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spelling pubmed-57057832017-12-04 Strong convergence of gradient projection method for generalized equilibrium problem in a Banach space Farid, Mohammad Irfan, Syed Shakaib Khan, Mohammad Firdosh Khan, Suhel Ahmad J Inequal Appl Research In this paper, we propose and analyze a hybrid iterative method for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of a variational inequality problem, and the set of fixed points of a relatively nonexpansive mapping in a real Banach space. Further, we prove the strong convergence of the sequences generated by the iterative scheme. Finally, we derive some consequences from our main result. Our work is an improvement and extension of some previously known results recently obtained by many authors. Springer International Publishing 2017-11-28 2017 /pmc/articles/PMC5705783/ /pubmed/29213202 http://dx.doi.org/10.1186/s13660-017-1574-x Text en © The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Farid, Mohammad
Irfan, Syed Shakaib
Khan, Mohammad Firdosh
Khan, Suhel Ahmad
Strong convergence of gradient projection method for generalized equilibrium problem in a Banach space
title Strong convergence of gradient projection method for generalized equilibrium problem in a Banach space
title_full Strong convergence of gradient projection method for generalized equilibrium problem in a Banach space
title_fullStr Strong convergence of gradient projection method for generalized equilibrium problem in a Banach space
title_full_unstemmed Strong convergence of gradient projection method for generalized equilibrium problem in a Banach space
title_short Strong convergence of gradient projection method for generalized equilibrium problem in a Banach space
title_sort strong convergence of gradient projection method for generalized equilibrium problem in a banach space
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5705783/
https://www.ncbi.nlm.nih.gov/pubmed/29213202
http://dx.doi.org/10.1186/s13660-017-1574-x
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