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

In this paper, we establish fixed point theorems for generalized nonlinearcontractive mappings using the concept of ω-distance in relational metric spaces. Thuswe 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 orderto revel the usefulness of such investigations, an application to first order periodicboundary value problem are given. Moreover, we furnish a non-trivial example todemonstrate the validity of our generalization over previous existing results.