Applying an Extended <em>β</em>-<em>ϕ</em>-Geraghty Contraction for Solving Coupled Ordinary Differential Equations

Abstract

In this paper, we introduce a new class of mappings called “generalized β-ϕ-Geraghty contraction-type mappings”. We use our new class to formulate and prove some coupled fixed points in the setting of partially ordered metric spaces. Our results generalize and unite several findings known in the literature. We also provide some examples to support and illustrate our theoretical results. Furthermore, we apply our results to discuss the existence and uniqueness of a solution to a coupled ordinary differential equation as an application of our finding.

Keywords

• extended <i>β</i>-<i>ϕ</i>-Geraghty contraction mapping
• generalized triangular <i>β</i>-admissible mapping
• coupled fixed point
• ordinary differential equation