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

Faizan Ahmad Khan (), Musaad S. Aldhabani (), Ahmed Alamer (), Esmail Alshaban, Fahad M. Alamrani and Hamid I. A. Mohammed
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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

Mathematics, 2023, vol. 11, issue 23, 1-11

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.

Keywords: binary relations; strict almost contractions; nonlinear Fredholm integral equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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