Existence of Best Proximity Point with an Application to Nonlinear Integral Equations

Abstract

Using the idea of modified $\mathrm{\varrho }$ -proximal admissible mappings, we derive some new best proximity point results for $\mathrm{\varrho }-\vartheta$ -contraction mappings in metric spaces. We also provide some illustrations to back up our work. As a result of our findings, several fixed-point results for such mappings are also found. We obtain the existence of a solution for nonlinear integral equations as an application.