Fixed point theorems for orthogonal F-contraction mappings on O-complete metric spaces

Abstract

In this paper, we introduce the notion of an orthogonal F-contraction mapping and establish some fixed point results for such contraction mappings in orthogonally metric spaces. Also, we give some examples which claim that the main results are generalizations of the Wardowski's fixed point theorem. As applications of the main results, we apply our main results to show the existence of a unique solution of the first-order ordinary differential equation.