Fixed and Periodic Point Results for Generalized Geraghty Contractions in Partial Metric Spaces with Application

Wudthichai Onsod, Teerapol Saleewong, Poom Kumam

Abstract

In this paper, by using the concept of $\alpha$-Garaghty contractions, we introduce a new concept of $(\mathcal{F},h)$-type Garaghty contraction via $\alpha$-admissible and $\mu$-subadmissible mappings. We prove some fixed point and periodic point results for such mappings in partial metric spaces. We also give an example for supporting the result. Moreover, an existence of solutions for nonlinear ordinary differential equation of second order with boundary conditions is obtained.