G-Complete G-Metric-Like Spaces, G-O-Completeness, and Some Common Fixed Point Theorems

Abstract

 

The notion of metric-like spaces was introduced by Amini-Harandi [Metric-like spaces, partial metric spaces and fixed points. Fixed Point Theory Appl. 2012, 204 (2012)]. Amini-Harandi defined the                          -completeness of metric-like spaces. In this paper, we introduce a notion of 0- -completeness which generalizes the notion of -completeness of Amini-Harandi, as well as the notion of 0-completeness of Romaguera[A Kirk type characterization of completeness for partial metric spaces. Fixed Point Theory Appl. 2010, 493298 (2010)] in the setting of G-metric spaces. We then use these basic notions and notations to generalize some results of Amini-Harandi.