Strong convergence theorems for a class of split feasibility problems and fixed point problem in Hilbert spaces

In this paper we consider a class of split feasibility problem by focusing on the solution sets of two important problems in the setting of Hilbert spaces. One of them is the set of zero points of the sum of two monotone operators and the other is the set of fixed points of mappings. By using the mo...

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Detalles Bibliográficos
Autores principales: Zhu, Jinhua, Tang, Jinfang, Chang, Shih-sen
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6208615/
https://www.ncbi.nlm.nih.gov/pubmed/30839719
http://dx.doi.org/10.1186/s13660-018-1881-x
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author Zhu, Jinhua
Tang, Jinfang
Chang, Shih-sen
author_facet Zhu, Jinhua
Tang, Jinfang
Chang, Shih-sen
author_sort Zhu, Jinhua
collection PubMed
description In this paper we consider a class of split feasibility problem by focusing on the solution sets of two important problems in the setting of Hilbert spaces. One of them is the set of zero points of the sum of two monotone operators and the other is the set of fixed points of mappings. By using the modified forward–backward splitting method, we propose a viscosity iterative algorithm. Under suitable conditions, some strong convergence theorems of the sequence generated by the algorithm to a common solution of the problem are proved. At the end of the paper, some applications and the constructed algorithm are also discussed.
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spelling pubmed-62086152018-11-09 Strong convergence theorems for a class of split feasibility problems and fixed point problem in Hilbert spaces Zhu, Jinhua Tang, Jinfang Chang, Shih-sen J Inequal Appl Research In this paper we consider a class of split feasibility problem by focusing on the solution sets of two important problems in the setting of Hilbert spaces. One of them is the set of zero points of the sum of two monotone operators and the other is the set of fixed points of mappings. By using the modified forward–backward splitting method, we propose a viscosity iterative algorithm. Under suitable conditions, some strong convergence theorems of the sequence generated by the algorithm to a common solution of the problem are proved. At the end of the paper, some applications and the constructed algorithm are also discussed. Springer International Publishing 2018-10-23 2018 /pmc/articles/PMC6208615/ /pubmed/30839719 http://dx.doi.org/10.1186/s13660-018-1881-x 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
Zhu, Jinhua
Tang, Jinfang
Chang, Shih-sen
Strong convergence theorems for a class of split feasibility problems and fixed point problem in Hilbert spaces
title Strong convergence theorems for a class of split feasibility problems and fixed point problem in Hilbert spaces
title_full Strong convergence theorems for a class of split feasibility problems and fixed point problem in Hilbert spaces
title_fullStr Strong convergence theorems for a class of split feasibility problems and fixed point problem in Hilbert spaces
title_full_unstemmed Strong convergence theorems for a class of split feasibility problems and fixed point problem in Hilbert spaces
title_short Strong convergence theorems for a class of split feasibility problems and fixed point problem in Hilbert spaces
title_sort strong convergence theorems for a class of split feasibility problems and fixed point problem in hilbert spaces
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6208615/
https://www.ncbi.nlm.nih.gov/pubmed/30839719
http://dx.doi.org/10.1186/s13660-018-1881-x
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AT tangjinfang strongconvergencetheoremsforaclassofsplitfeasibilityproblemsandfixedpointprobleminhilbertspaces
AT changshihsen strongconvergencetheoremsforaclassofsplitfeasibilityproblemsandfixedpointprobleminhilbertspaces

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