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.