Weak orthogonal metric spaces and fixed point results

Abstract

In this article we extend the notion of orthogonal metric space to weak orthogonal metric space. Then we establish fixed point results for a mapping satisfying a more general contraction condition. Several nontrivial examples are given in support of our obtained results. Moreover, we are able to answer of the open question posed by Eshaghi et al. [On orthogonal sets and Banach fixed point theorem, Fixed Point Theory, 18(2017), 569-578].