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

Shamoona Jabeen, Zhiming Zheng, Mutti-Ur Rehman, Wei Wei and Jehad Alzabut
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Shamoona Jabeen: School of Mathematical Sciences, Beihang University, Beijing 100191, China
Zhiming Zheng: School of Mathematical Sciences, Beihang University, Beijing 100191, China
Mutti-Ur Rehman: Department of Mathematics, Sukkur IBA University, Sukkur 65200, Pakistan
Wei Wei: School of Mathematical Sciences, Beihang University, Beijing 100191, China
Jehad Alzabut: Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia

Mathematics, 2021, vol. 9, issue 5, 1-14

Abstract: 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.

Keywords: fuzzy cone metric space; fixed point; weak-contraction; graph structure (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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