Fixed Point of (<i>α</i>,<i>β</i>)-Admissible Generalized Geraghty <i>F</i>-Contraction with Application

Abstract

In this paper, we introduce some new types of extended Geraghty contractions, called (α,β)-admissible generalized Geraghty F-contractions, and prove some fixed point results for such contractions in the setting of partial b-metric spaces. Moreover, based on the obtained fixed point results and the property of symmetry, we inaugurate a fixed point result for graphic generalized Geraghty F-contractions defined on partial metric spaces endowed with a directed graph. As an application, we examine the existence of a unique solution to the first-order periodic boundary value by the obtained fixed point result. Moreover, some examples are presented to illustrate the validity of the new results.

Keywords

• fixed point
• partial metric spaces
• <i>b</i>-metric spaces
• <i>F</i>-contraction
• (<i>α</i>,<i>β</i>)-admissible