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Generalized Weak Contractions Involving a Pair of Auxiliary Functions via Locally Transitive Binary Relations and Applications to Boundary Value Problems

Author

Listed:
  • Nidal H. E. Eljaneid

    (Department of Mathematics, Science Faculty, University of Tabuk, Tabuk 71491, Saudi Arabia)

  • Esmail Alshaban

    (Department of Mathematics, Science Faculty, University of Tabuk, Tabuk 71491, Saudi Arabia)

  • Adel Alatawi

    (Department of Mathematics, Science Faculty, University of Tabuk, Tabuk 71491, Saudi Arabia)

  • Montaser Saudi Ali

    (Department of Mathematics, Science Faculty, University of Tabuk, Tabuk 71491, Saudi Arabia)

  • Saud S. Alsharari

    (Department of Mathematics, Science Faculty, Northern Border University, Arar 73213, Saudi Arabia)

  • Faizan Ahmad Khan

    (Department of Mathematics, Science Faculty, University of Tabuk, Tabuk 71491, Saudi Arabia)

Abstract

The intent of this paper was to investigate the fixed-point results under relation-theoretic generalized weak contractivity condition employing a pair of auxiliary functions ϕ and ψ verifying appropriate properties. In proving our outcomes, we observed that the partial-ordered relation (even, transitive relation) adopted by earlier authors can be weakened to the extent of a locally ϝ -transitive binary relation. The findings proved herewith generalize, extend, improve, and unify a number of existing outcomes. To validate of our findings, we offer a number of illustrative examples. Our outcomes assist us to figure out the existence and uniqueness of solutions to a boundary value problem.

Suggested Citation

  • Nidal H. E. Eljaneid & Esmail Alshaban & Adel Alatawi & Montaser Saudi Ali & Saud S. Alsharari & Faizan Ahmad Khan, 2025. "Generalized Weak Contractions Involving a Pair of Auxiliary Functions via Locally Transitive Binary Relations and Applications to Boundary Value Problems," Mathematics, MDPI, vol. 13(1), pages 1-13, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:1:p:163-:d:1560614
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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. Salma Aljawi & Izhar Uddin, 2024. "Relation-Theoretic Nonlinear Almost Contractions with an Application to Boundary Value Problems," Mathematics, MDPI, vol. 12(9), pages 1-10, April.
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