Simulative Suzuki-Gerghaty type contraction with $\mathcal{C}$-class functions and applications

TL;DR

This paper introduces a new type of contraction mapping using simulation functions and -class functions, proving fixed point existence and applying it to nonlinear integral equations.

Contribution

It presents a novel Suzuki-Gerghaty type contraction framework with -class functions, extending fixed point theory and solving nonlinear Hammerstein integral equations.

Findings

Established fixed point existence under the new contraction conditions

Provided an example demonstrating the validity of the results

Applied the theory to solve nonlinear Hammerstein integral equations

Abstract

The aim of this paper is to introduce the notion of a Suzuki-Gerghaty type contractive mapping via simulation function along with $\mathcal{C}$-class functions and prove the existence of fixed point result. An example is given to show the validity of our results given herein. Moreover, we prove the existence of solution of nonlinear Hammerstein integral equation.