Fixed points for hybrid pair of compatible mappings in partial metric spaces

Abstract

In this paper coincidence and fixed point theorems for a pair of single-valued and multi-valued compatible mappings on complete partial metric spaces are presented. The notion of compatible mappings for a pair of single-valued and multi-valued mappings proved to be very useful as the existing metric fixed point theory contains numerous fixed point results for pair(s) of mappings established under compatibility condition and its generaliztions. Partial metric spaces are one of generalizations of the notion of a metric space that allows non-zero self distance. The existing metric fixed point theory approaches, are adapted to establish the results. The main result generalizes, in particular, a fixed point theorem due to Kaneko and Sessa for hybrid pair of compatible mappings. An illustrative example is also provided.