Common Fixed Points of Set –Valued  Mappings on  Partial  b - Metric  Spaces

In this work, the Banach contraction principle is generalized to a new formula. Then, it is used to give the guarantee conditions for the existence of common fixed point for set valued mappings defined on complete partial b-metric spaces. In addition, some results in connection with the existence of a fixed point for a set-valued mapping defined on a partial b-metric space are given. Some examples are established to illustrate our results.