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On Banach fixed point theorems for partial metric spaces. (English) Zbl 1087.54020
Summary: We prove several generalizations of the Banach fixed point theorem for partial metric spaces (in the sense of O’Neill) given in [S. Oltra and O. Valero, Rend. Ist. Math. Univ. Triest. 36, 17–26 (2004; Zbl 1080.54030)], obtaining as a particular case of our results the Banach fixed-point theorem of S. G. Matthews [Ann. N. Y. Acad. Sci. 728, 183–197 (1994; Zbl 0911.54025)], and some well-known classical fixed-point theorems when the partial metric is, in fact, a metric.
##### MSC:
 54H25 Fixed-point and coincidence theorems in topological spaces 54E50 Complete metric spaces 54E99 Topological spaces with richer structures 68Q55 Semantics
##### Keywords:
dualistic partial metric; complete; quasi-metric