## Abstract

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.

## Authors

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

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

Valeriu Anisiu

Valeriu Anisiu

## Keywords

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

## References

[1] O. Acar, I. Altun, S. Romaguera, Caristi’s type mappings on complete partial metric spaces, Fixed Point Theory, 14(1)(2013), 3-10.

[2] M.-C. Anisiu, V. Anisiu, Z. Kasa, Total palindrome complexity of finite words, Discr. Math., 310(2010), 109-114.

[3] J. Caristi, Fixed point theorems for mappings satisfying inwardness conditions, Trans. Amer. Math. Soc., 215(1976), 241-251.

[4] S¸. Cobza¸s, Completeness in quasi-metric spaces and Ekeland Variational Principle, Topol. Appl., 158(2011), 1073-1084.

[5] R.H. Haghi, Sh. Rezapour, N. Shahzad, Be careful on partial metric fixed point results, Topology and its Applications, 160(3)(2013), 450-454.

[6] H.P.A. Kunzi, Non-symmetric distances and their associated topologies: About the origins of basic ideas in the area of asymmetric topology, in Handbook of the history of general topology, eds. Aull, C. E., Lowen, R., 3, 853-968, Springer Science+ Business Media Dordrecht, 2001.

[7] S.G. Matthews, Partial metric spaces, 8th British Colloquium for Theoretical Computer Science, March 1992. In Research Report 212, Dept. of Computer Science, University of Warwick, 1992.

[8] S.G. Matthews, Partial metric topology, In: Proceedings of the 8th Summer Conference on General Topology and Applications, Annals of the New York Academy of Sciences, 728(1994), 183-197.

[9] S. Romaguera, A Kirk type characterization of completeness for partial metric spaces, Fixed Point Theory Appl., (2010) Article ID 493298, 6 pp.

[10] B. Samet, Existence and uniqueness of solutions to a system of functional equations and applications to partial metric spaces, Fixed Point Theory, 14(2)(2013), 473-481.

[11] M. Schellekens, The Smyth completion: a common foundation for denotational semantics and complexity analysis, Electronic Notes in Theoretical Computer Science, 1(1995), 535-556.

[12] M. Turinici, Function contractive maps in partial metric spaces, ROMAI J., 8(1), 189-207.

[13] W.A. Wilson, On quasi-metric spaces, Amer. J. Math., 53(1931), 675-684.

##### Cite this paper as:

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

## About this paper

##### Journal

Fixed Point Theory

##### Publisher Name

Casa Cărții de Știință Cluj-Napoca

##### DOI

Not available yet.

##### Print ISSN

1583-5022

##### Online ISSN

2066-9208