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Extensions of the Zamfirescu theorem to partial metric spaces. (English) Zbl 1255.54022
Summary: {\it T. Zamfirescu} [Arch. Math. 23, 292--298 (1972; Zbl 0239.54030)] obtained a very interesting fixed point theorem on complete metric spaces by combining the results of S. Banach, R. Kannan and S. K.\thinspace Chatterjea. {\it S. G. Matthews} [Ann. N. Y. Acad. Sci. 728, 183--197 (1994; Zbl 0911.54025)] introduced and studied the concept of partial metric spaces, and obtained a Banach type fixed point theorem on complete partial metric spaces. In this paper, we study new extensions of the Zamfirescu theorem to the context of partial metric spaces, and among other things, we give some generalized versions of the fixed point theorem of Matthews. The theory is illustrated by some examples.

54H25Fixed-point and coincidence theorems in topological spaces
54E35Metric spaces, metrizability
Full Text: DOI
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