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

Subject classification

6N40; 47H10; 54H25; 46T99

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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. https://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. https://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. https://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. https://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. https://doi.org/10.1155/2011/812690

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. https://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. https://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. https://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. https://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. https://doi.org/10.4995/agt.2005.1957

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. https://doi.org/10.4995/agt.2005.1954

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