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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Shamoona Jabeen & Zhiming Zheng & Mutti-Ur Rehman & Wei Wei & Jehad Alzabut, 2021. "Some Fixed Point Results of Weak-Fuzzy Graphical Contraction Mappings with Application to Integral Equations," Mathematics, MDPI, vol. 9(5), pages 1-14, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:541-:d:510524
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    References listed on IDEAS

    as
    1. Ravi P. Agarwal & Nawab Hussain & Mohamed-Aziz Taoudi, 2012. "Fixed Point Theorems in Ordered Banach Spaces and Applications to Nonlinear Integral Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, July.
    2. Radenović, Stojan & Zoto, Kastriot & Dedović, Nebojša & Šešum-Cavic, Vesna & Hojat Ansari, Arslan, 2019. "Bhaskar-Guo-Lakshmikantam-Ćirić type results via new functions with applications to integral equations," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 75-87.
    3. M. R. Alfuraidan & M. A. Khamsi, 2014. "Caristi Fixed Point Theorem in Metric Spaces with a Graph," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-5, March.
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