Weak partial metric spaces and some fixed point results

Ishak Altun, Gonca Durmaz
DOI: https://doi.org/10.4995/agt.2012.1628

Abstract

The concept of partial metric p on a nonempty set X was introduced by Matthews. One of the most interesting properties of a partial metric is that p(x, x) may not be zero for x e X. Also, each partial metric p on a nonempty set X generates a T0 topology on X. By omitting the small self-distance axiom of partial metric, Heckmann defined the weak partial metric space. In the present paper, we give some fixed point results on weak partial metric spaces.

Keywords

Fixed point; Partial metric space; Weak partial metric space

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References

I. Altun and A. Erduran, Fixed point theorems for monotone mappings on partial metric spaces, Fixed Point Theory and Applications (2011), Article ID 508730, 10 pp.

I. Altun and H. Simsek, Some fixed point theorems on dualistic partial metric spaces, J. Adv. Math. Stud. 1 (2008), 1–8.

I. Altun, F. Sola and H. Simsek, Generalized contractions on partial metric spaces, Topology and its Applications 157 (2010), 2778–2785. http://dx.doi.org/10.1016/j.topol.2010.08.017

V. Berinde, Iterative Approximation of Fixed Points, Springer -Verlag Berlin Heidelberg, 2007.

M. H. Escardo, Pcf Extended with real numbers, Theoretical Computer Sciences 162 (1996), 79–115. http://dx.doi.org/10.1016/0304-3975(95)00250-2

G. E. Hardy, T. D. Rogers, A generalization of a fixed point theorem of Reich, Canad. Math. Bull. 16 (1973), 201–206. http://dx.doi.org/10.4153/CMB-1973-036-0

R. Heckmann, Approximation of metric spaces by partial metric spaces, Appl. Categ. Structures 7 (1999), 71–83.

S. G. Matthews, Partial metric topology, Proc. 8th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci. 728 (1994), 183–197. http://dx.doi.org/10.1023/A:1008684018933

S. Oltra and O. Valero, Banach’s fixed point theorem for partial metric spaces, Rend. Istid. Math. Univ. Trieste 36 (2004), 17–26.

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

O. Valero, On Banach fixed point theorems for partial metric spaces, Appl. General Topology 6 (2005), 229–240.

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1. Common fixed point of mappings satisfying almost generalized (S,T)-contractive condition in partially ordered partial metric spaces
N. Shobkolaei, S. Sedghi, J.R. Roshan, I. Altun
Applied Mathematics and Computation  vol: 219  issue: 2  first page: 443  year: 2012  
doi: 10.1016/j.amc.2012.06.063



Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt