Existence, well-posedness of coupled fixed points and application to nonlinear integral equations

Abstract We investigate a fixed point problem for coupled Geraghty type contraction in a metric space with a binary relation. The role of the binary relation is to restrict the scope of the contraction to smaller number of ordered pairs. Such possibilities have been explored for different types of c...

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Autores principales:	Choudhury,Binayak S., Metiya,Nikhilesh, Kundu,Sunirmal
Lenguaje:	English
Publicado:	Universidad de La Frontera. Departamento de Matemática y Estadística. 2021
Materias:	Metric space coupled fixed point well-posedness application
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462021000100171
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spelling	oai:scielo:S0719-064620210001001712021-05-11Existence, well-posedness of coupled fixed points and application to nonlinear integral equationsChoudhury,Binayak S.Metiya,NikhileshKundu,Sunirmal Metric space coupled fixed point well-posedness application Abstract We investigate a fixed point problem for coupled Geraghty type contraction in a metric space with a binary relation. The role of the binary relation is to restrict the scope of the contraction to smaller number of ordered pairs. Such possibilities have been explored for different types of contractions in recent times which has led to the emergence of relational fixed point theory. Geraghty type contractions arose in the literatures as a part of research seeking the replacement contraction constants by appropriate functions. Also coupled fixed point problems have evoked much interest in recent times. Combining the above trends we formulate and solve the fixed point problem mentioned above. Further we show that with some additional conditions such solution is unique. Well-posedness of the problem is investigated. An illustrative example is discussed. The consequences of the results are discussed considering α-dominated mappings and graphs on the metric space. Finally we apply our result to show the existence of solution of some system of nonlinear integral equations.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.23 n.1 20212021-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462021000100171en10.4067/S0719-06462021000100171
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Metric space coupled fixed point well-posedness application
spellingShingle	Metric space coupled fixed point well-posedness application Choudhury,Binayak S. Metiya,Nikhilesh Kundu,Sunirmal Existence, well-posedness of coupled fixed points and application to nonlinear integral equations
description	Abstract We investigate a fixed point problem for coupled Geraghty type contraction in a metric space with a binary relation. The role of the binary relation is to restrict the scope of the contraction to smaller number of ordered pairs. Such possibilities have been explored for different types of contractions in recent times which has led to the emergence of relational fixed point theory. Geraghty type contractions arose in the literatures as a part of research seeking the replacement contraction constants by appropriate functions. Also coupled fixed point problems have evoked much interest in recent times. Combining the above trends we formulate and solve the fixed point problem mentioned above. Further we show that with some additional conditions such solution is unique. Well-posedness of the problem is investigated. An illustrative example is discussed. The consequences of the results are discussed considering α-dominated mappings and graphs on the metric space. Finally we apply our result to show the existence of solution of some system of nonlinear integral equations.
author	Choudhury,Binayak S. Metiya,Nikhilesh Kundu,Sunirmal
author_facet	Choudhury,Binayak S. Metiya,Nikhilesh Kundu,Sunirmal
author_sort	Choudhury,Binayak S.
title	Existence, well-posedness of coupled fixed points and application to nonlinear integral equations
title_short	Existence, well-posedness of coupled fixed points and application to nonlinear integral equations
title_full	Existence, well-posedness of coupled fixed points and application to nonlinear integral equations
title_fullStr	Existence, well-posedness of coupled fixed points and application to nonlinear integral equations
title_full_unstemmed	Existence, well-posedness of coupled fixed points and application to nonlinear integral equations
title_sort	existence, well-posedness of coupled fixed points and application to nonlinear integral equations
publisher	Universidad de La Frontera. Departamento de Matemática y Estadística.
publishDate	2021
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462021000100171
work_keys_str_mv	AT choudhurybinayaks existencewellposednessofcoupledfixedpointsandapplicationtononlinearintegralequations AT metiyanikhilesh existencewellposednessofcoupledfixedpointsandapplicationtononlinearintegralequations AT kundusunirmal existencewellposednessofcoupledfixedpointsandapplicationtononlinearintegralequations
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Existence, well-posedness of coupled fixed points and application to nonlinear integral equations

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