Approximating distance between sets by multivalued coupling with application to uniformly convex Banach spaces

In this paper, our aim is to ascertain the distance between two sets iteratively in two simultaneous ways with the help of a multivalued coupling define for this purpose. We define the best proximity points of such couplings that realize the distance between two sets. Our main theorem is deduced in...

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Autores principales: Choudhury, Binayak S., Maity, Pranati, Metiya, Nikhilesh, Postolache, Mihai
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5996065/
https://www.ncbi.nlm.nih.gov/pubmed/30137724
http://dx.doi.org/10.1186/s13660-018-1720-0
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author Choudhury, Binayak S.
Maity, Pranati
Metiya, Nikhilesh
Postolache, Mihai
author_facet Choudhury, Binayak S.
Maity, Pranati
Metiya, Nikhilesh
Postolache, Mihai
author_sort Choudhury, Binayak S.
collection PubMed
description In this paper, our aim is to ascertain the distance between two sets iteratively in two simultaneous ways with the help of a multivalued coupling define for this purpose. We define the best proximity points of such couplings that realize the distance between two sets. Our main theorem is deduced in metric spaces. As an application, we obtain the corresponding results in uniformly convex Banach spaces using the geometry of the space. We discuss two examples.
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spelling pubmed-59960652018-06-25 Approximating distance between sets by multivalued coupling with application to uniformly convex Banach spaces Choudhury, Binayak S. Maity, Pranati Metiya, Nikhilesh Postolache, Mihai J Inequal Appl Research In this paper, our aim is to ascertain the distance between two sets iteratively in two simultaneous ways with the help of a multivalued coupling define for this purpose. We define the best proximity points of such couplings that realize the distance between two sets. Our main theorem is deduced in metric spaces. As an application, we obtain the corresponding results in uniformly convex Banach spaces using the geometry of the space. We discuss two examples. Springer International Publishing 2018-06-11 2018 /pmc/articles/PMC5996065/ /pubmed/30137724 http://dx.doi.org/10.1186/s13660-018-1720-0 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
Choudhury, Binayak S.
Maity, Pranati
Metiya, Nikhilesh
Postolache, Mihai
Approximating distance between sets by multivalued coupling with application to uniformly convex Banach spaces
title Approximating distance between sets by multivalued coupling with application to uniformly convex Banach spaces
title_full Approximating distance between sets by multivalued coupling with application to uniformly convex Banach spaces
title_fullStr Approximating distance between sets by multivalued coupling with application to uniformly convex Banach spaces
title_full_unstemmed Approximating distance between sets by multivalued coupling with application to uniformly convex Banach spaces
title_short Approximating distance between sets by multivalued coupling with application to uniformly convex Banach spaces
title_sort approximating distance between sets by multivalued coupling with application to uniformly convex banach spaces
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5996065/
https://www.ncbi.nlm.nih.gov/pubmed/30137724
http://dx.doi.org/10.1186/s13660-018-1720-0
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