On a fixed point theorem with application to functional equations

Abstract

The purpose of this paper is to study behavior of a rational type contraction introduced in [A fixed point theorem for contractions of rational type in partially ordered metric spaces, Ann. Univ. Ferrara, 2013, 59, 251-258] in context of ordered dualistic partial metric spaces and to investigate sufficient conditions for the existence of a fixed point in this space. These results extend various comparable results, existing in the literature. We give examples to explain our findings. We apply our result to prove the existence of the solution of functional equation.