Fixed point results for Ʇ_Hθ- contractive mappings in orthogonal metric spaces

Abstract

The main purpose of this research is to extend some fixed point results in orthogonal metric spaces. For this purpose, first, we investigate new mappings in this spaces. We introduce the new notions of functions. Then by using it, we define contractive mappings and then we establish and prove some fixed point theorems for such mappings in orthogonal metric spaces. Then by utilizing examples of the function we deduce some new consequences for these fixed point theorems. Also in this research paper we will give applications. As first application, we will show that many fixed point results in metric spaces endowed with a graph G can be deduced easily from fixed point theorems in orthogonal metric spaces. As another application, we will show that many fixed point results in partially ordered metric spaces can be deduced easily from fixed point theorems in orthogonal metric spaces. Indeed, in this paper in addition to extend some fixed point results in orthogonal metric spaces, we will show that our obtained results unify many fixed point results.