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Almost Nonlinear Contractions under Locally Finitely Transitive Relations with Applications to Integral Equations

Author

Listed:
  • Faizan Ahmad Khan

    (Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia)

  • Musaad S. Aldhabani

    (Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia)

  • Ahmed Alamer

    (Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia)

  • Esmail Alshaban

    (Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia)

  • Fahad M. Alamrani

    (Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia)

  • Hamid I. A. Mohammed

    (Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia
    Department of Mathematics, University of Bahri, Khartoum 11111, Sudan)

Abstract

This article consists of some new fixed point theorems verifying relation-theoretic strict almost nonlinear contractions that are preserved by a locally finitely transitive relation. Our results improve certain well-known results in the literature. To confirm the reliability of our results, some examples are delivered. We carry out our findings to solve a nonlinear Fredholm integral equation.

Suggested Citation

  • Faizan Ahmad Khan & Musaad S. Aldhabani & Ahmed Alamer & Esmail Alshaban & Fahad M. Alamrani & Hamid I. A. Mohammed, 2023. "Almost Nonlinear Contractions under Locally Finitely Transitive Relations with Applications to Integral Equations," Mathematics, MDPI, vol. 11(23), pages 1-11, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4749-:d:1286873
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