Fixed Point Theorems in Relational Metric Spaces with an Application to Boundary Value Problems

In this paper, we establish fixed point theorems for generalized nonlinear contractive mappings using the concept of w-distance in relational metric spaces. Thus we generalize the recent results of Senapati and Dey [J. Fixed Point Theory Appl. 19, 2945-2961 (2017)] and many other important results relevant to this literature. In order to revel the usefulness of such investigations, an application to first order periodic boundary value problem are given. Moreover, we furnish a non-trivial example to demonstrate the validity of our generalization over previous existing results.