Gerghaty type results via simulation and $\mathcal{C}$-class functions with application

TL;DR

This paper introduces Gerghaty type fixed point results using simulation functions and $ ext{C}$-class functions, demonstrating their applicability in solving boundary value problems in metric spaces.

Contribution

It extends fixed point theory by incorporating simulation and $ ext{C}$-class functions to establish new existence results in metric and ordered spaces.

Findings

Established fixed point theorems for Gerghaty type mappings.

Provided an example validating the theoretical results.

Applied the results to solve a boundary value problem.

Abstract

In this paper we study the notion of Gerghaty type contractive mapping via simulation function along with $\mathcal{C}$-class functions and prove the existence of several fixed point results in ordinary and partially ordered metric spaces. An example is given to show the validity of our results given herein. Moreover, existence of solution of two-point boundary value second order nonlinear differential equation is obtain.