| Summary: | In this paper, we introduce some new types of extended Geraghty contractions, called <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>)</mo></mrow></semantics></math></inline-formula>-admissible generalized Geraghty <i>F</i>-contractions, and prove some fixed point results for such contractions in the setting of partial <i>b</i>-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 <i>F</i>-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.
|
|---|