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

Abstract

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In this paper, we establish fixed point theorems for generalized nonlinear\ncontractive mappings using the concept of \u03c9-distance in relational metric spaces. Thus\nwe generalize the recent results of Senapati and Dey [J. Fixed Point Theory Appl. 19,\n2945-2961 (2017)] and many other important results relevant to this literature. In order\nto reveal the usefulness of such investigations, an application to first order periodic\nboundary value problem are given. Moreover, we furnish a non-trivial example to\ndemonstrate the validity of our generalization over previous existing results.<\/p>"