Fixed point theorems via w-distance in relational metric spaces with an application

Abstract

In this paper, we establish fixed point theorems for generalized nonlinear contractive mappings using the concept of w-distance on metric spaces endowed with an arbitrary binary relation. Our fixed point theorems generalize recent results of Senapati and Dey [J. Fixed Point Theory Appl. 19, 2945-2961 (2017)] and many other important results of the existing literature. Moreover, in order to revel the usability of our findings an example and an application to the first order periodic boundary value problem are given.