Applicability of Fixed Point Results in Boundary Value Problems Satisfying Generalized Geraghty-Type Contraction

Amrish Handa

Abstract

We establish a unique common fixed point theorem for G-non-decreasing mappings under Geraghty-type contraction on partially ordered metric spaces. With the help of the obtain results, we derive a coupled fixed point result and achieve the solution for periodic boundary value problems. We also give an example to show the applicability of the obtained results. Our results modify and generalize various well-known results.