Some fixed point theorems on the class of comparable partial metric spaces

Erdal Karapinar

Abstract

In this paper we present existence and uniqueness criteria of a fixed point for a self mapping on a non-empty set endowed with two comparable partial metrics.

Keywords

Partial metric space; Fixed point theory; Comparable metrics

Full Text:

PDF

References

T. Abdeljawad, E. Karapınar, K. Tas, Existence and uniqueness of common fixed point on partial metric spaces, Appl. Math. Lett. 24, no. 11 (2011), 1894–1899. http://dx.doi.org/10.1016/j.aml.2011.05.014

I. Altun, F. Sola and H. Simsek, Generalized contractions on partial metric spaces, Topology Appl. 157, no. 18 (2010), 2778–2785. http://dx.doi.org/10.1016/j.topol.2010.08.017

E. Karapınar, Generalizations of Caristi Kirk’s Theorem on partial metric spaces, Fixed Point Theory Appl. 2011:4. http://dx.doi.org/10.1186/1687-1812-2011-4

E. Karapınar and I. M. Erhan, Fixed point theorems for operators on partial metric spaces, Appl. Math. Lett. 24, no. 11 (2011), 1900–1904. http://dx.doi.org/10.1016/j.aml.2011.05.013

E. Karapınar, Weak o-contraction on partial contraction and existence of fixed points in partially ordered sets, Mathematica Aeterna 1(4),(2011), 237-244.

E. Karapınar, Weak o-contraction on partial metric spaces, J. Comput. Anal. Appl. (in press).

R. Kopperman, S. G. Matthews and H. Pajoohesh, What do partial metrics represent, Spatial representation: discrete vs. continuous computational models, Dagstuhl Seminar Proceedings, No. 04351, Internationales Begegnungs und Forschungszentrum für Informatik (IBFI), Schloss Dagstuhl, Germany, (2005).

H.-P. A. Künzi, H. Pajoohesh and M.P. Schellekens, Partial quasi-metrics, Theor. Comput. Sci. 365, no. 3 (2006), 237–246. http://dx.doi.org/10.1016/j.tcs.2006.07.050

M. G. Maia, Un’osservazione sulle contrazioni metriche, Rend. Sem. Mat. Univ. Padova 40 (1968), 139–143.

S. G. Matthews, Partial metric topology, Research Report 212, Dept. of Computer Science, University of Warwick, 1992.

S. G. Matthews, Partial metric topology, in: General Topology and its Applications, Proc. 8th Summer Conf., Queen’s College (1992), Annals of the New York Academy of Sciences, 728 (1994), 183–197. http://dx.doi.org/10.1111/j.1749-6632.1994.tb44144.x

S. J. O’Neill, Two topologies are better than one, Tech. report, University of Warwick, Coventry, UK, http://www.dcs.warwick.ac.uk/reports/283.html, 1995.

S. Romaguera and M. Schellekens, Weightable quasi-metric semigroup and semilattices, Electron. Notes Theor. Comput. Sci. 40 (2001), 347–358. http://dx.doi.org/10.1016/S1571-0661(05)80061-1

M. P. Schellekens, A characterization of partial metrizability: domains are quantifiable, Theor. Comput. Sci. 305, no. 1-3 (2003), 409–432. http://dx.doi.org/10.1016/S0304-3975(02)00705-3

S. Oltra and O. Valero, Banach’s fixed point theorem for partial metric spaces, Rend. Ist. Mat. Univ. Trieste 36, no. 1-2 (2004), 17–26.

O. Valero, On Banach fixed point theorems for partial metric spaces, Appl. Gen. Topol 6, no. 2 (2005), 229–240.

S. Oltra, S. Romaguera and E. A. Sánchez-Pérez, The canonical partial metric and uniform convexity on normed spaces, Appl. Gen. Topol. 6, no. 2 (2005), 185–194.

Abstract Views

1113
Metrics Loading ...

Metrics powered by PLOS ALM




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