On the characterizations of partial metrics and quasimetrics

We present the relationship between the notion of partial metric, which has applications in Computer Science, that of quasimetric (which lacks symmetry) and that of standard metric. In this process the nonexpansive functions play an important role. We give some simple formulations of the sequence convergence and of the 0-completeness in partial metric spaces. We apply the results to the characterization of completeness in terms of Caristi’s theorem in quasimetric spaces.

Mira-Cristiana Anisiu
T. Popoviciu Institute of Numerical Analysis, Romanian Academy, P.O. Box 68, 400110 Cluj-Napoca, Romania

Valeriu Anisiu
Department of Mathematics, Babes-Bolyai University, 1 Kogalniceanu St., 400084 Cluj-Napoca, Romania

metric spaces; partial metric; quasimetric; fixed points; nonexpansive mappings; Caristi’s theorem.

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Mira-Cristiana Anisiu, Valeriu Anisiu, On the characterizations of partial metrics and quasimetrics, Fixed Point Theory 17 (1) (2016), 37-46

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