IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i5p541-d510524.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/5/541/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/5/541/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hasanen A. Hammad & Manuel De la Sen, 2019. "PPF-Dependent Fixed Point Results for New Multi-Valued Generalized F -Contraction in the Razumikhin Class with an Application," Mathematics, MDPI, vol. 7(1), pages 1-16, January.
    2. Mohadeshe Paknazar & Manuel De la Sen, 2017. "Best Proximity Point Results in Non-Archimedean Modular Metric Space," Mathematics, MDPI, vol. 5(2), pages 1-20, April.
    3. Hussain, Nawab & Kutbi, M.A. & Salimi, Peyman, 2020. "Global optimal solutions for proximal fuzzy contractions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    4. Hamed H Al-Sulami & Jamshaid Ahmad & Nawab Hussain & Abdul Latif, 2019. "Solutions to Fredholm Integral Inclusions via Generalized Fuzzy Contractions," Mathematics, MDPI, vol. 7(9), pages 1-19, September.
    5. Hasanen A. Hammad & Amal A. Khalil, 2020. "The Technique of Quadruple Fixed Points for Solving Functional Integral Equations under a Measure of Noncompactness," Mathematics, MDPI, vol. 8(12), pages 1-21, November.
    6. Deepmala, 2014. "Existence Theorems for Solvability of a Functional Equation Arising in Dynamic Programming," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2014, pages 1-9, April.
    7. Angamuthu Muraliraj & Ravichandran Thangathamizh & Nikola Popovic & Ana Savic & Stojan Radenovic, 2023. "The First Rational Type Revised Fuzzy-Contractions in Revised Fuzzy Metric Spaces with an Applications," Mathematics, MDPI, vol. 11(10), pages 1-11, May.
    8. Hasanen Abuelmagd Hammad & Manuel De la Sen, 2019. "A Coupled Fixed Point Technique for Solving Coupled Systems of Functional and Nonlinear Integral Equations," Mathematics, MDPI, vol. 7(7), pages 1-18, July.
    9. Karim Chaira & Abderrahim Eladraoui & Mustapha Kabil & Samih Lazaiz, 2018. "Extension of Kirk-Saliga Fixed Point Theorem in a Metric Space with a Reflexive Digraph," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2018, pages 1-6, February.
    10. Yeol Je Cho & Shin Min Kang & Peyman Salimi, 2018. "Some PPF Dependent Fixed Point Theorems for Generalized α - F -Contractions in Banach Spaces and Applications," Mathematics, MDPI, vol. 6(11), pages 1-19, November.
    11. P. Charoensawan & W. Atiponrat, 2017. "Common Fixed Point and Coupled Coincidence Point Theorems for Geraghty’s Type Contraction Mapping with Two Metrics Endowed with a Directed Graph," Journal of Mathematics, Hindawi, vol. 2017, pages 1-9, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:541-:d:510524. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.