Some Fixed Point Results of Weak-Fuzzy Graphical Contraction Mappings with Application to Integral Equations

Some Fixed Point Results of Weak-Fuzzy Graphical Contraction Mappings with Application to Integral Equations

The present paper aims to introduce the concept of weak-fuzzy contraction mappings in the graph structure within the context of fuzzy cone metric spaces. We prove some fixed point results endowed with a graph using weak-fuzzy contractions. By relaxing the continuity condition of mappings involved, o...

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Main Authors: Shamoona Jabeen, Zhiming Zheng, Mutti-Ur Rehman, Wei Wei, Jehad Alzabut
Format: Article
Language:English
Published: MDPI AG 2021-03-01
Series:Mathematics
Subjects:
fuzzy cone metric space
fixed point
weak-contraction
graph structure
Online Access:https://www.mdpi.com/2227-7390/9/5/541
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spelling doaj-af332f0a6d474cc9a48fc2e20a6f74332021-03-05T00:06:04ZengMDPI AGMathematics2227-73902021-03-01954154110.3390/math9050541Some Fixed Point Results of Weak-Fuzzy Graphical Contraction Mappings with Application to Integral EquationsShamoona Jabeen0Zhiming Zheng1Mutti-Ur Rehman2Wei Wei3Jehad Alzabut4School of Mathematical Sciences, Beihang University, Beijing 100191, ChinaSchool of Mathematical Sciences, Beihang University, Beijing 100191, ChinaDepartment of Mathematics, Sukkur IBA University, Sukkur 65200, PakistanSchool of Mathematical Sciences, Beihang University, Beijing 100191, ChinaDepartment of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaThe present paper aims to introduce the concept of weak-fuzzy contraction mappings in the graph structure within the context of fuzzy cone metric spaces. We prove some fixed point results endowed with a graph using weak-fuzzy contractions. By relaxing the continuity condition of mappings involved, our results enrich and generalize some well-known results in fixed point theory. With the help of new lemmas, our proofs are straight forward. We furnish the validity of our findings with appropriate examples. This approach is completely new and will be beneficial for the future aspects of the related study. We provide an application of integral equations to illustrate the usability of our theory.https://www.mdpi.com/2227-7390/9/5/541fuzzy cone metric spacefixed pointweak-contractiongraph structure
collection DOAJ
language English
format Article
sources DOAJ
author Shamoona Jabeen
Zhiming Zheng
Mutti-Ur Rehman
Wei Wei
Jehad Alzabut
spellingShingle Shamoona Jabeen
Zhiming Zheng
Mutti-Ur Rehman
Wei Wei
Jehad Alzabut
Some Fixed Point Results of Weak-Fuzzy Graphical Contraction Mappings with Application to Integral Equations
Mathematics
fuzzy cone metric space
fixed point
weak-contraction
graph structure
author_facet Shamoona Jabeen
Zhiming Zheng
Mutti-Ur Rehman
Wei Wei
Jehad Alzabut
author_sort Shamoona Jabeen
title Some Fixed Point Results of Weak-Fuzzy Graphical Contraction Mappings with Application to Integral Equations
title_short Some Fixed Point Results of Weak-Fuzzy Graphical Contraction Mappings with Application to Integral Equations
title_full Some Fixed Point Results of Weak-Fuzzy Graphical Contraction Mappings with Application to Integral Equations
title_fullStr Some Fixed Point Results of Weak-Fuzzy Graphical Contraction Mappings with Application to Integral Equations
title_full_unstemmed Some Fixed Point Results of Weak-Fuzzy Graphical Contraction Mappings with Application to Integral Equations
title_sort some fixed point results of weak-fuzzy graphical contraction mappings with application to integral equations
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2021-03-01
description The present paper aims to introduce the concept of weak-fuzzy contraction mappings in the graph structure within the context of fuzzy cone metric spaces. We prove some fixed point results endowed with a graph using weak-fuzzy contractions. By relaxing the continuity condition of mappings involved, our results enrich and generalize some well-known results in fixed point theory. With the help of new lemmas, our proofs are straight forward. We furnish the validity of our findings with appropriate examples. This approach is completely new and will be beneficial for the future aspects of the related study. We provide an application of integral equations to illustrate the usability of our theory.
topic fuzzy cone metric space
fixed point
weak-contraction
graph structure
url https://www.mdpi.com/2227-7390/9/5/541
work_keys_str_mv AT shamoonajabeen somefixedpointresultsofweakfuzzygraphicalcontractionmappingswithapplicationtointegralequations
AT zhimingzheng somefixedpointresultsofweakfuzzygraphicalcontractionmappingswithapplicationtointegralequations
AT muttiurrehman somefixedpointresultsofweakfuzzygraphicalcontractionmappingswithapplicationtointegralequations
AT weiwei somefixedpointresultsofweakfuzzygraphicalcontractionmappingswithapplicationtointegralequations
AT jehadalzabut somefixedpointresultsofweakfuzzygraphicalcontractionmappingswithapplicationtointegralequations
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