Extended Rectangular <i>M<sub>rc</sub></i>-Metric Spaces and Fixed Point Results

Extended Rectangular <i>M<sub>rc</sub></i>-Metric Spaces and Fixed Point Results

In this paper, we enlarge the classes of rectangular <em>M<sub>b</sub></em>-metric spaces and extended<br />rectangular <em>b</em>-metric spaces by considering the class of extended rectangular <em>M<sub>rc</sub></em>-metric spaces<...

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Main Authors: Mohammad Asim, Kottakkaran Sooppy Nisar, Ahmed Morsy, M. Imdad
Format: Article
Language:English
Published: MDPI AG 2019-11-01
Series:Mathematics
Subjects:
extended rectangular <i>>m<subrc</sub></i>-metric space
fixed point
Online Access:https://www.mdpi.com/2227-7390/7/12/1136
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spelling doaj-59c59710ddbd4c5797649af4ab2670702020-11-25T01:18:31ZengMDPI AGMathematics2227-73902019-11-01712113610.3390/math7121136math7121136Extended Rectangular <i>M<sub>rc</sub></i>-Metric Spaces and Fixed Point ResultsMohammad Asim0Kottakkaran Sooppy Nisar1Ahmed Morsy2M. Imdad3Department of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaDepartment of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi ArabiaDepartment of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi ArabiaDepartment of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaIn this paper, we enlarge the classes of rectangular <em>M<sub>b</sub></em>-metric spaces and extended<br />rectangular <em>b</em>-metric spaces by considering the class of extended rectangular <em>M<sub>rc</sub></em>-metric spaces<br />and utilize the same to prove an analogue of Banach contraction principle in such spaces. We adopt<br />an example to highlight the utility of our main result. Finally, we apply our result to examine the<br />existence and uniqueness of solution for a system of Fredholm integral equation.https://www.mdpi.com/2227-7390/7/12/1136extended rectangular <i>>m<subrc</sub></i>-metric spacefixed point
collection DOAJ
language English
format Article
sources DOAJ
author Mohammad Asim
Kottakkaran Sooppy Nisar
Ahmed Morsy
M. Imdad
spellingShingle Mohammad Asim
Kottakkaran Sooppy Nisar
Ahmed Morsy
M. Imdad
Extended Rectangular <i>M<sub>rc</sub></i>-Metric Spaces and Fixed Point Results
Mathematics
extended rectangular <i>>m<subrc</sub></i>-metric space
fixed point
author_facet Mohammad Asim
Kottakkaran Sooppy Nisar
Ahmed Morsy
M. Imdad
author_sort Mohammad Asim
title Extended Rectangular <i>M<sub>rc</sub></i>-Metric Spaces and Fixed Point Results
title_short Extended Rectangular <i>M<sub>rc</sub></i>-Metric Spaces and Fixed Point Results
title_full Extended Rectangular <i>M<sub>rc</sub></i>-Metric Spaces and Fixed Point Results
title_fullStr Extended Rectangular <i>M<sub>rc</sub></i>-Metric Spaces and Fixed Point Results
title_full_unstemmed Extended Rectangular <i>M<sub>rc</sub></i>-Metric Spaces and Fixed Point Results
title_sort extended rectangular <i>m<sub>rc</sub></i>-metric spaces and fixed point results
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2019-11-01
description In this paper, we enlarge the classes of rectangular <em>M<sub>b</sub></em>-metric spaces and extended<br />rectangular <em>b</em>-metric spaces by considering the class of extended rectangular <em>M<sub>rc</sub></em>-metric spaces<br />and utilize the same to prove an analogue of Banach contraction principle in such spaces. We adopt<br />an example to highlight the utility of our main result. Finally, we apply our result to examine the<br />existence and uniqueness of solution for a system of Fredholm integral equation.
topic extended rectangular <i>>m<subrc</sub></i>-metric space
fixed point
url https://www.mdpi.com/2227-7390/7/12/1136
work_keys_str_mv AT mohammadasim extendedrectangularimsubrcsubimetricspacesandfixedpointresults
AT kottakkaransooppynisar extendedrectangularimsubrcsubimetricspacesandfixedpointresults
AT ahmedmorsy extendedrectangularimsubrcsubimetricspacesandfixedpointresults
AT mimdad extendedrectangularimsubrcsubimetricspacesandfixedpointresults
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