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A generalized contraction principle with control functions on partial metric spaces. (English) Zbl 1238.54017
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 $\varphi$ and $\psi$ 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.
##### MSC:
 54H25 Fixed-point and coincidence theorems in topological spaces 47H10 Fixed point theorems for nonlinear operators on topological linear spaces