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

Abstract 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 de...

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Main Authors:	Binayak S. Choudhury, Pranati Maity, Nikhilesh Metiya, Mihai Postolache
Format:	Article
Language:	English
Published:	Springer 2018-06-01
Series:	Journal of Inequalities and Applications
Subjects:	Metric spaces Coupling Best proximity pair Optimal approximate solution Uniformly convex Banach space
Online Access:	http://link.springer.com/article/10.1186/s13660-018-1720-0

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spelling	doaj-art-ccf5f42b85c54a26afb39b8030b1b21e2018-08-15T21:06:58ZengSpringerJournal of Inequalities and Applications1029-242X2018-06-012018111510.1186/s13660-018-1720-0Approximating distance between sets by multivalued coupling with application to uniformly convex Banach spacesBinayak S. Choudhury0Pranati Maity1Nikhilesh Metiya2Mihai Postolache3Department of Mathematics, Indian Institute of Engineering Science and TechnologyDepartment of Mathematics, National Institute of TechnologyDepartment of Mathematics, Sovarani Memorial CollegeChina Medical UniversityAbstract 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.http://link.springer.com/article/10.1186/s13660-018-1720-0Metric spacesCouplingBest proximity pairOptimal approximate solutionUniformly convex Banach space
institution	Open Data Bank
collection	Open Access Journals
building	Directory of Open Access Journals
language	English
format	Article
author	Binayak S. Choudhury Pranati Maity Nikhilesh Metiya Mihai Postolache
spellingShingle	Binayak S. Choudhury Pranati Maity Nikhilesh Metiya Mihai Postolache Approximating distance between sets by multivalued coupling with application to uniformly convex Banach spaces Journal of Inequalities and Applications Metric spaces Coupling Best proximity pair Optimal approximate solution Uniformly convex Banach space
author_facet	Binayak S. Choudhury Pranati Maity Nikhilesh Metiya Mihai Postolache
author_sort	Binayak S. Choudhury
title	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_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_sort	approximating distance between sets by multivalued coupling with application to uniformly convex banach spaces
publisher	Springer
series	Journal of Inequalities and Applications
issn	1029-242X
publishDate	2018-06-01
description	Abstract 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.
topic	Metric spaces Coupling Best proximity pair Optimal approximate solution Uniformly convex Banach space
url	http://link.springer.com/article/10.1186/s13660-018-1720-0
_version_	1612706877689298944

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

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