Summary: Partial metric spaces were introduced by S. G. Matthews
[in: Papers on general topology and applications. Papers from the 8th summer conference at Queens College, New York, NY, USA, June 18–20, 1992. New York, NY: The New York Academy of Sciences. Ann. N. Y. Acad. Sci. 728, 183–197 (1994; Zbl 0911.54025
)] as a part of the study of denotational semantics of data flow networks. We prove a generalized contraction principle with control functions
on partial metric spaces. The theorems we prove generalize many previously obtained results. We also give some examples showing that our theorems are indeed proper extensions.