Strong convergence theorems by hybrid and shrinking projection methods for sums of two monotone operators

In this paper, we introduce two iterative algorithms for finding the solution of the sum of two monotone operators by using hybrid projection methods and shrinking projection methods. Under some suitable conditions, we prove strong convergence theorems of such sequences to the solution of the sum of...

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Detalles Bibliográficos
Autores principales: Yuying, Tadchai, Plubtieng, Somyot
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5388757/
https://www.ncbi.nlm.nih.gov/pubmed/28458482
http://dx.doi.org/10.1186/s13660-017-1338-7
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author Yuying, Tadchai
Plubtieng, Somyot
author_facet Yuying, Tadchai
Plubtieng, Somyot
author_sort Yuying, Tadchai
collection PubMed
description In this paper, we introduce two iterative algorithms for finding the solution of the sum of two monotone operators by using hybrid projection methods and shrinking projection methods. Under some suitable conditions, we prove strong convergence theorems of such sequences to the solution of the sum of an inverse-strongly monotone and a maximal monotone operator. Finally, we present a numerical result of our algorithm which is defined by the hybrid method.
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spelling pubmed-53887572017-04-27 Strong convergence theorems by hybrid and shrinking projection methods for sums of two monotone operators Yuying, Tadchai Plubtieng, Somyot J Inequal Appl Research In this paper, we introduce two iterative algorithms for finding the solution of the sum of two monotone operators by using hybrid projection methods and shrinking projection methods. Under some suitable conditions, we prove strong convergence theorems of such sequences to the solution of the sum of an inverse-strongly monotone and a maximal monotone operator. Finally, we present a numerical result of our algorithm which is defined by the hybrid method. Springer International Publishing 2017-04-11 2017 /pmc/articles/PMC5388757/ /pubmed/28458482 http://dx.doi.org/10.1186/s13660-017-1338-7 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
Yuying, Tadchai
Plubtieng, Somyot
Strong convergence theorems by hybrid and shrinking projection methods for sums of two monotone operators
title Strong convergence theorems by hybrid and shrinking projection methods for sums of two monotone operators
title_full Strong convergence theorems by hybrid and shrinking projection methods for sums of two monotone operators
title_fullStr Strong convergence theorems by hybrid and shrinking projection methods for sums of two monotone operators
title_full_unstemmed Strong convergence theorems by hybrid and shrinking projection methods for sums of two monotone operators
title_short Strong convergence theorems by hybrid and shrinking projection methods for sums of two monotone operators
title_sort strong convergence theorems by hybrid and shrinking projection methods for sums of two monotone operators
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5388757/
https://www.ncbi.nlm.nih.gov/pubmed/28458482
http://dx.doi.org/10.1186/s13660-017-1338-7
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