Common Fixed Points of g-quasicontractions for Faithly Compatible Mappings in 0-complete Partial Metric Spaces

Abstract

Common fixed point results are obtained in 0-complete partial metric spaces under various contractive conditions, including g-quasicontractions and mappings with a contractive iterate. In this way, several results obtained recently are generalized. In this paper we introduce a generalization of the concept of compatible mappings, and using that condition in partial ordered metric spaces, we obtain some new fixed point theorems under both contractive and noncontractive conditions, which may allow the existence of a common fixed point or the existence of multiple fixed or coincidence points. We also manifest that the new concept is a necessary condition for the existence of a common fixed point.