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

Document Type : Research Paper


1 Department of Mathematics, University of Sargodha, Sargodha-40100, Pakistan

2 Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd 35, Serbia


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.