Almost Nonlinear Contractions of Pant Type Employing Locally Finitely Transitive Relations with an Application to Nonlinear Integral Equations

Faizan Ahmad Khan (), Abdulrahman F. Aljohani, Adel Alatawi, Fahad M. Alamrani, Mohammed Zayed Alruwaytie and Esmail Alshaban ()
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Faizan Ahmad Khan: Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia
Abdulrahman F. Aljohani: Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia
Adel Alatawi: Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia
Fahad M. Alamrani: Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia
Mohammed Zayed Alruwaytie: Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia
Esmail Alshaban: Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia

Mathematics, 2025, vol. 13, issue 19, 1-16

Abstract: In this research, a few metrical fixed-point outcomes consisting of an almost nonlinear Pant-type contraction employing a locally finitely transitive relation have been established. The findings of our research extrapolate, unify, develop, and improve a number of previously mentioned results. In the present investigation, we formulate a fixed-point finding for almost nonlinear Pant-type contractions in abstract metric space. To assist our study, we formulate numerous examples to illustrate our outcomes. Using our findings, we describe the existence and uniqueness of solutions to a nonlinear Fredholm integral equation.

Keywords: strict almost contractions; fixed-point theorems; ?-transitive relations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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