The viscosity iterative algorithms for the implicit midpoint rule of nonexpansive mappings in uniformly smooth Banach spaces

The aim of this paper is to introduce a viscosity iterative algorithm for the implicit midpoint rule of nonexpansive mappings in uniformly smooth spaces. Under some appropriate conditions on the parameters, we prove some strong convergence theorems. As applications, we apply our main results to solv...

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Detalles Bibliográficos
Autores principales: Luo, Ping, Cai, Gang, Shehu, Yekini
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5489619/
https://www.ncbi.nlm.nih.gov/pubmed/28680256
http://dx.doi.org/10.1186/s13660-017-1426-8
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author Luo, Ping
Cai, Gang
Shehu, Yekini
author_facet Luo, Ping
Cai, Gang
Shehu, Yekini
author_sort Luo, Ping
collection PubMed
description The aim of this paper is to introduce a viscosity iterative algorithm for the implicit midpoint rule of nonexpansive mappings in uniformly smooth spaces. Under some appropriate conditions on the parameters, we prove some strong convergence theorems. As applications, we apply our main results to solving fixed point problems of strict pseudocontractive mappings, variational inequality problems in Banach spaces and equilibrium problems in Hilbert spaces. Finally, we give some numerical examples for supporting our main results.
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spelling pubmed-54896192017-07-03 The viscosity iterative algorithms for the implicit midpoint rule of nonexpansive mappings in uniformly smooth Banach spaces Luo, Ping Cai, Gang Shehu, Yekini J Inequal Appl Research The aim of this paper is to introduce a viscosity iterative algorithm for the implicit midpoint rule of nonexpansive mappings in uniformly smooth spaces. Under some appropriate conditions on the parameters, we prove some strong convergence theorems. As applications, we apply our main results to solving fixed point problems of strict pseudocontractive mappings, variational inequality problems in Banach spaces and equilibrium problems in Hilbert spaces. Finally, we give some numerical examples for supporting our main results. Springer International Publishing 2017-06-28 2017 /pmc/articles/PMC5489619/ /pubmed/28680256 http://dx.doi.org/10.1186/s13660-017-1426-8 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
Luo, Ping
Cai, Gang
Shehu, Yekini
The viscosity iterative algorithms for the implicit midpoint rule of nonexpansive mappings in uniformly smooth Banach spaces
title The viscosity iterative algorithms for the implicit midpoint rule of nonexpansive mappings in uniformly smooth Banach spaces
title_full The viscosity iterative algorithms for the implicit midpoint rule of nonexpansive mappings in uniformly smooth Banach spaces
title_fullStr The viscosity iterative algorithms for the implicit midpoint rule of nonexpansive mappings in uniformly smooth Banach spaces
title_full_unstemmed The viscosity iterative algorithms for the implicit midpoint rule of nonexpansive mappings in uniformly smooth Banach spaces
title_short The viscosity iterative algorithms for the implicit midpoint rule of nonexpansive mappings in uniformly smooth Banach spaces
title_sort viscosity iterative algorithms for the implicit midpoint rule of nonexpansive mappings in uniformly smooth banach spaces
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5489619/
https://www.ncbi.nlm.nih.gov/pubmed/28680256
http://dx.doi.org/10.1186/s13660-017-1426-8
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