Generalization of the Carsti,s Condition on Partial b- Metric Spaces

Abstract

Caristi’s Theorem plays as an important rule to guaranties the existence of the fixed point for a single valued mapping and a Set-valued mapping that defined on complete partial b-metric spaces. In our paper some new generalizations of Caristi’s condition have been introduced and we use them in them in our work to give the guaranties in which the single and set-valued mappings have a fixed point on partial b- metric spaces. As well as, some applications have been studied to illustrate the mechanism of using these generalizations of Caristi’s condition.