Geraghty Type Generalized F‐Contractions and Related Applications in Partial b‐Metric Spaces

The purpose of this paper is to introduce new concepts of (α,β)-admissible Geraghty type generalized F-contraction and to prove that some fixed point results for such mappings are in the perspective of partial b-metric space. As an application, we inaugurate new fixed point results for Geraghty type generalized graphic F-contraction defined on partial metric space endowed with a directed graph. On the other hand, one more application to the existence and uniqueness of a solution for the first-order periodic boundary value problem is also provided. Our findings encompass various generalizations of the Banach contraction principle on metric space, partial metric space, and partial b-metric space. Moreover, some examples are presented to illustrate the usability of the new theory