Some fixed point theorems on orthogonal metric spaces via extensions of orthogonal contractions

Abstract

Orthogonal metric space is a considerable generalization of a usual metric space obtained by establishing a perpendicular relation on a set. Very recently, the notions of orthogonality of the set and orthogonality of the metric space are described and notable fixed point theorems are given in orthogonal metric spaces. Some fixed point theorems for the generalizations of contraction principle via altering distance functions on orthogonal metric spaces are presented and proved in this paper. Furthermore, an example is presented to clarify these theorems.