Multivariate systems of nonexpansive operator equations and iterative algorithms for solving them in uniformly convex and uniformly smooth Banach spaces with applications

We prove some existence theorems for solutions of a certain system of multivariate nonexpansive operator equations and calculate the solutions by using the generalized Mann and Halpern iterative algorithms in uniformly convex and uniformly smooth Banach spaces. The results of this paper improve and...

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Detalles Bibliográficos
Autores principales: Xu, Yongchun, Guan, Jinyu, Tang, Yanxia, Su, Yongfu
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5811615/
https://www.ncbi.nlm.nih.gov/pubmed/29479164
http://dx.doi.org/10.1186/s13660-018-1629-7
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author Xu, Yongchun
Guan, Jinyu
Tang, Yanxia
Su, Yongfu
author_facet Xu, Yongchun
Guan, Jinyu
Tang, Yanxia
Su, Yongfu
author_sort Xu, Yongchun
collection PubMed
description We prove some existence theorems for solutions of a certain system of multivariate nonexpansive operator equations and calculate the solutions by using the generalized Mann and Halpern iterative algorithms in uniformly convex and uniformly smooth Banach spaces. The results of this paper improve and extend the previously known ones in the literature.
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spelling pubmed-58116152018-02-23 Multivariate systems of nonexpansive operator equations and iterative algorithms for solving them in uniformly convex and uniformly smooth Banach spaces with applications Xu, Yongchun Guan, Jinyu Tang, Yanxia Su, Yongfu J Inequal Appl Research We prove some existence theorems for solutions of a certain system of multivariate nonexpansive operator equations and calculate the solutions by using the generalized Mann and Halpern iterative algorithms in uniformly convex and uniformly smooth Banach spaces. The results of this paper improve and extend the previously known ones in the literature. Springer International Publishing 2018-02-13 2018 /pmc/articles/PMC5811615/ /pubmed/29479164 http://dx.doi.org/10.1186/s13660-018-1629-7 Text en © The Author(s) 2018 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
Xu, Yongchun
Guan, Jinyu
Tang, Yanxia
Su, Yongfu
Multivariate systems of nonexpansive operator equations and iterative algorithms for solving them in uniformly convex and uniformly smooth Banach spaces with applications
title Multivariate systems of nonexpansive operator equations and iterative algorithms for solving them in uniformly convex and uniformly smooth Banach spaces with applications
title_full Multivariate systems of nonexpansive operator equations and iterative algorithms for solving them in uniformly convex and uniformly smooth Banach spaces with applications
title_fullStr Multivariate systems of nonexpansive operator equations and iterative algorithms for solving them in uniformly convex and uniformly smooth Banach spaces with applications
title_full_unstemmed Multivariate systems of nonexpansive operator equations and iterative algorithms for solving them in uniformly convex and uniformly smooth Banach spaces with applications
title_short Multivariate systems of nonexpansive operator equations and iterative algorithms for solving them in uniformly convex and uniformly smooth Banach spaces with applications
title_sort multivariate systems of nonexpansive operator equations and iterative algorithms for solving them in uniformly convex and uniformly smooth banach spaces with applications
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5811615/
https://www.ncbi.nlm.nih.gov/pubmed/29479164
http://dx.doi.org/10.1186/s13660-018-1629-7
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