Common Fixed Point Results for Almost <i>ℛ<sub>g</sub></i>-Geraghty Type Contraction Mappings in <i>b</i><sub>2</sub>-Metric Spaces with an Application to Integral Equations

Common Fixed Point Results for Almost <i>ℛ<sub>g</sub></i>-Geraghty Type Contraction Mappings in <i>b</i><sub>2</sub>-Metric Spaces with an Application to Integral Equations

In this paper, we define almost <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">R</mi><mi>g</mi></msub></semantics></math></i...

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Main Authors: Samera M. Saleh, Salvatore Sessa, Waleed M. Alfaqih, Fawzia Shaddad
Format: Article
Language:English
Published: MDPI AG 2021-05-01
Series:Axioms
Subjects:
<i>b</i><sub>2</sub>-metric space
fixed point
binary relation
almost <i>ℛ<sub>g</sub></i>-Geraghty type contraction
Online Access:https://www.mdpi.com/2075-1680/10/2/101
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spelling doaj-700b717a0b5c4c86a02e55721fa503992021-06-01T00:55:02ZengMDPI AGAxioms2075-16802021-05-011010110110.3390/axioms10020101Common Fixed Point Results for Almost <i>ℛ<sub>g</sub></i>-Geraghty Type Contraction Mappings in <i>b</i><sub>2</sub>-Metric Spaces with an Application to Integral EquationsSamera M. Saleh0Salvatore Sessa1Waleed M. Alfaqih2Fawzia Shaddad3Department of Mathematics, Faculty of Science, Taiz University, Taiz 6803, YemenDipartimento di Architettura, Università degli Studi di Napoli Federico II, Via Toledo 402, 80134 Napoli, ItalyDepartment of Mathematics, Hajjah University, Hajjah 1729, YemenDepartment of Mathematics, Sana’a University, Sana’a 1247, YemenIn this paper, we define almost <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">R</mi><mi>g</mi></msub></semantics></math></inline-formula>-Geraghty type contractions and utilize the same to establish some coincidence and common fixed point results in the setting of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>b</mi><mn>2</mn></msub></semantics></math></inline-formula>-metric spaces endowed with binary relations. As consequences of our newly proved results, we deduce some coincidence and common fixed point results for almost <i>g</i>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula> Geraghty type contraction mappings in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>b</mi><mn>2</mn></msub></semantics></math></inline-formula>-metric spaces. In addition, we derive some coincidence and common fixed point results in partially ordered <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>b</mi><mn>2</mn></msub></semantics></math></inline-formula>-metric spaces. Moreover, to show the utility of our main results, we provide an example and an application to non-linear integral equations.https://www.mdpi.com/2075-1680/10/2/101<i>b</i><sub>2</sub>-metric spacefixed pointbinary relationalmost <i>ℛ<sub>g</sub></i>-Geraghty type contraction
collection DOAJ
language English
format Article
sources DOAJ
author Samera M. Saleh
Salvatore Sessa
Waleed M. Alfaqih
Fawzia Shaddad
spellingShingle Samera M. Saleh
Salvatore Sessa
Waleed M. Alfaqih
Fawzia Shaddad
Common Fixed Point Results for Almost <i>ℛ<sub>g</sub></i>-Geraghty Type Contraction Mappings in <i>b</i><sub>2</sub>-Metric Spaces with an Application to Integral Equations
Axioms
<i>b</i><sub>2</sub>-metric space
fixed point
binary relation
almost <i>ℛ<sub>g</sub></i>-Geraghty type contraction
author_facet Samera M. Saleh
Salvatore Sessa
Waleed M. Alfaqih
Fawzia Shaddad
author_sort Samera M. Saleh
title Common Fixed Point Results for Almost <i>ℛ<sub>g</sub></i>-Geraghty Type Contraction Mappings in <i>b</i><sub>2</sub>-Metric Spaces with an Application to Integral Equations
title_short Common Fixed Point Results for Almost <i>ℛ<sub>g</sub></i>-Geraghty Type Contraction Mappings in <i>b</i><sub>2</sub>-Metric Spaces with an Application to Integral Equations
title_full Common Fixed Point Results for Almost <i>ℛ<sub>g</sub></i>-Geraghty Type Contraction Mappings in <i>b</i><sub>2</sub>-Metric Spaces with an Application to Integral Equations
title_fullStr Common Fixed Point Results for Almost <i>ℛ<sub>g</sub></i>-Geraghty Type Contraction Mappings in <i>b</i><sub>2</sub>-Metric Spaces with an Application to Integral Equations
title_full_unstemmed Common Fixed Point Results for Almost <i>ℛ<sub>g</sub></i>-Geraghty Type Contraction Mappings in <i>b</i><sub>2</sub>-Metric Spaces with an Application to Integral Equations
title_sort common fixed point results for almost <i>ℛ<sub>g</sub></i>-geraghty type contraction mappings in <i>b</i><sub>2</sub>-metric spaces with an application to integral equations
publisher MDPI AG
series Axioms
issn 2075-1680
publishDate 2021-05-01
description In this paper, we define almost <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">R</mi><mi>g</mi></msub></semantics></math></inline-formula>-Geraghty type contractions and utilize the same to establish some coincidence and common fixed point results in the setting of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>b</mi><mn>2</mn></msub></semantics></math></inline-formula>-metric spaces endowed with binary relations. As consequences of our newly proved results, we deduce some coincidence and common fixed point results for almost <i>g</i>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula> Geraghty type contraction mappings in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>b</mi><mn>2</mn></msub></semantics></math></inline-formula>-metric spaces. In addition, we derive some coincidence and common fixed point results in partially ordered <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>b</mi><mn>2</mn></msub></semantics></math></inline-formula>-metric spaces. Moreover, to show the utility of our main results, we provide an example and an application to non-linear integral equations.
topic <i>b</i><sub>2</sub>-metric space
fixed point
binary relation
almost <i>ℛ<sub>g</sub></i>-Geraghty type contraction
url https://www.mdpi.com/2075-1680/10/2/101
work_keys_str_mv AT sameramsaleh commonfixedpointresultsforalmostirsubgsubigeraghtytypecontractionmappingsinibisub2submetricspaceswithanapplicationtointegralequations
AT salvatoresessa commonfixedpointresultsforalmostirsubgsubigeraghtytypecontractionmappingsinibisub2submetricspaceswithanapplicationtointegralequations
AT waleedmalfaqih commonfixedpointresultsforalmostirsubgsubigeraghtytypecontractionmappingsinibisub2submetricspaceswithanapplicationtointegralequations
AT fawziashaddad commonfixedpointresultsforalmostirsubgsubigeraghtytypecontractionmappingsinibisub2submetricspaceswithanapplicationtointegralequations
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