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.


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Volume 12, Issue 1
May 2021
Pages 1057-1071
  • Receive Date: 25 September 2018
  • Revise Date: 16 November 2019
  • Accept Date: 22 November 2019