Hybrid algorithm for common solution of monotone inclusion problem and fixed point problem and applications to variational inequalities

The aim of this paper is to investigate hybrid algorithm for a common zero point of the sum of two monotone operators which is also a fixed point of a family of countable quasi-nonexpansive mappings. We point out two incorrect proof in paper (Hecai in Fixed Point Theory Appl 2013:11, 2013). Further,...

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Detalles Bibliográficos
Autores principales: Zhang, Jingling, Jiang, Nan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2016
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4916130/
https://www.ncbi.nlm.nih.gov/pubmed/27390644
http://dx.doi.org/10.1186/s40064-016-2389-9
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author Zhang, Jingling
Jiang, Nan
author_facet Zhang, Jingling
Jiang, Nan
author_sort Zhang, Jingling
collection PubMed
description The aim of this paper is to investigate hybrid algorithm for a common zero point of the sum of two monotone operators which is also a fixed point of a family of countable quasi-nonexpansive mappings. We point out two incorrect proof in paper (Hecai in Fixed Point Theory Appl 2013:11, 2013). Further, we modify and generalize the results of Hecai’s paper, in which only a quasi-nonexpansive mapping was considered. In addition, two family of countable quasi-nonexpansive mappings with uniform closeness examples are provided to demonstrate our results. Finally, the results are applied to variational inequalities.
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spelling pubmed-49161302016-07-07 Hybrid algorithm for common solution of monotone inclusion problem and fixed point problem and applications to variational inequalities Zhang, Jingling Jiang, Nan Springerplus Research The aim of this paper is to investigate hybrid algorithm for a common zero point of the sum of two monotone operators which is also a fixed point of a family of countable quasi-nonexpansive mappings. We point out two incorrect proof in paper (Hecai in Fixed Point Theory Appl 2013:11, 2013). Further, we modify and generalize the results of Hecai’s paper, in which only a quasi-nonexpansive mapping was considered. In addition, two family of countable quasi-nonexpansive mappings with uniform closeness examples are provided to demonstrate our results. Finally, the results are applied to variational inequalities. Springer International Publishing 2016-06-21 /pmc/articles/PMC4916130/ /pubmed/27390644 http://dx.doi.org/10.1186/s40064-016-2389-9 Text en © The Author(s) 2016 Open AccessThis 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
Zhang, Jingling
Jiang, Nan
Hybrid algorithm for common solution of monotone inclusion problem and fixed point problem and applications to variational inequalities
title Hybrid algorithm for common solution of monotone inclusion problem and fixed point problem and applications to variational inequalities
title_full Hybrid algorithm for common solution of monotone inclusion problem and fixed point problem and applications to variational inequalities
title_fullStr Hybrid algorithm for common solution of monotone inclusion problem and fixed point problem and applications to variational inequalities
title_full_unstemmed Hybrid algorithm for common solution of monotone inclusion problem and fixed point problem and applications to variational inequalities
title_short Hybrid algorithm for common solution of monotone inclusion problem and fixed point problem and applications to variational inequalities
title_sort hybrid algorithm for common solution of monotone inclusion problem and fixed point problem and applications to variational inequalities
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4916130/
https://www.ncbi.nlm.nih.gov/pubmed/27390644
http://dx.doi.org/10.1186/s40064-016-2389-9
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AT jiangnan hybridalgorithmforcommonsolutionofmonotoneinclusionproblemandfixedpointproblemandapplicationstovariationalinequalities

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