Common Fixed Points for Weakly Compatible Mappings in Partial Metric Spaces

Abstract

In many situations the arising mappings need not be self-mappings. It is well known that metrically convex metric spaces are desirable for the study of fixed points of non-self mappings. Partial metric spaces are generalization of the notion of a metric space that allows non-zero self distance. In this paper, we present a common fixed point theorem for weakly compatible mappings on complete metrically convex partial metric spaces. Our main result generalizes a common metric fixed point theorem due to ´Ciri´c and Ume, which is an extension of a metric fixed point theorem due to Rhoades, to partial metric spaces.