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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

international journal of analysis

Geraghty Type Generalized <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>F</mml:mi></mml:mrow></mml:math>-Contractions and Related Applications in Partial <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:math>-Metric Spaces

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