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A Class of Relational Functional Contractions with Applications to Nonlinear Integral Equations

Author

Listed:
  • Khursheed J. Ansari

    (Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia)

  • Salvatore Sessa

    (Department of Architecture, University of Naples Federico II, 80134 Naples, Italy)

  • Aftab Alam

    (Centre of Professional Courses, Aligarh Muslim University, Aligarh 202002, India)

Abstract

In this article, we investigate some fixed-point results under certain functional contractive mappings in a relation metric space. In the process, we utilize more general contraction condition which must be verified for comparative elements only. Our results enrich, modify, refine, unify and sharpen several existing fixed-point results. We construct some examples in support of our results. To attest to the applicability of our results, we establish the existence and uniqueness of theorems regarding the solutions of certain nonlinear integral equations.

Suggested Citation

  • Khursheed J. Ansari & Salvatore Sessa & Aftab Alam, 2023. "A Class of Relational Functional Contractions with Applications to Nonlinear Integral Equations," Mathematics, MDPI, vol. 11(15), pages 1-11, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:15:p:3408-:d:1210900
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    References listed on IDEAS

    as
    1. Asik Hossain & Aftab Alam & Salvatore Sessa & Qamrul Haque Khan, 2023. "Relation-Theoretic Weak Contractions and Applications," Mathematics, MDPI, vol. 11(9), pages 1-15, April.
    2. Ebrahem Ateatullah Algehyne & Musaad Sabih Aldhabani & Faizan Ahmad Khan, 2023. "Relational Contractions Involving (c)-Comparison Functions with Applications to Boundary Value Problems," Mathematics, MDPI, vol. 11(6), pages 1-11, March.
    Full references (including those not matched with items on IDEAS)

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