Extensions of the Zamfirescu theorem to partial metric spaces. (English) Zbl 1255.54022

Ilić, Dejan; Pavlović, Vladimir; Rakočević, Vladimir

Math. Comput. Modelling 55, No. 3-4, 801-809 (2012).

Summary: 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.Chatterjea. 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.

MSC:

54H25	Fixed-point and coincidence theorems (topological aspects)
54E35	Metric spaces, metrizability

Keywords:

fixed point; Banach contraction; partial metric space; Zamfirescu theorem; Zamfirescu operator

Citations:

Zbl 0239.54030; Zbl 0911.54025

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