Nonlinear Almost Contractions of Pant Type Under Binary Relations with an Application to Boundary Value Problems

Esmail Alshaban, Adel Alatawi, Fahad M. Alamrani, Ahmed Alamer (), Naif N. Alrshidi () and Faizan Ahmad Khan ()
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Esmail Alshaban: 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
Ahmed Alamer: Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia
Naif N. Alrshidi: Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia
Faizan Ahmad Khan: Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia

Mathematics, 2025, vol. 13, issue 6, 1-16

Abstract: In this article, we prove certain fixed point findings for a nonlinear almost contraction map of the Pant type in a metric space endowed with a binary relation. The outcomes presented here expand, develop, enhance, and consolidate several existing findings. With a view to arguing for our findings, we furnish a few examples. As an application of our outcomes, we discuss the existence of a unique solution of a boundary value problem of the first order.

Keywords: fixed points; ϕ -contraction maps; boundary value problems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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