On Banach fixed point theorems for partial metric spaces

Oscar Valero


In this paper we prove several generalizations of the Banach fixed point theorem for partial metric spaces (in the sense of O’Neill) given in, obtaining as a particular case of our results the Banach fixed point theorem of Matthews ([12]), and some well-known classical fixed point theorems when the partial metric is, in fact, a metric.


Dualistic partial metric; Partial metric; Complete; Quasi-metric; Fixed point

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Ravi P. Agarwal, Maria Meehan, Donal O’Regan, Fixed Point Theory and Applications, Cambridge University Press, Cambridge, 2001.

D. W. Boyd, J. S. Wong, On nonlinear contractions, Proc. Amer. Math. Soc. 20 (1969), 458-464. http://dx.doi.org/10.1090/S0002-9939-1969-0239559-9

M. A. Bukatin, J. S. Scott, Towards computing distances between programs via Scott domains, in: Logical Foundations of Computer Sicence, Lecture Notes in Computer Science (eds. S. Adian and A. Nerode), vol. 1234, Springer (Berlin, 1997), pp. 33-43. http://dx.doi.org/10.1007/3-540-63045-7_4

M. A. Bukatin, S. Y. Shorina, Partial metrics and co-continuous valuations, in: Foundations of Software Science and Computation Structures, Lecture Notes in Computer Science (ed. M. Nivat), vol. 1378, Springer (Berlin, 1998), pp. 33-43. http://dx.doi.org/10.1007/BFb0053546

S. K. Chatterjee, Fixed point theorems, Rend. Acad. Bulgare Sc. 25 (1972), 727-730.

L. B. Ciric, Generalized contractions and fixed point theorems, Publ. Inst. Math. 12 (1971), 20-26.

J. Dugundji, A. Granas, Fixed Point Theory, Monografie Matematyczne, Vol. 61, Polish Scientific Publishers, 1982.

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

P. Fletcher, W. F. Lindgren, Quasi-Uniform Spaces, Marcel Dekker, New York, 1982.

R. Kannan, Some results on fixed points, Bull. Calcuta Math,. Soc. 60 (1968), 71-76.

H.P.A. Künzi, Nonsymmetric 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. C.E. Aull and R. Lowen), vol. 3, Kluwer Acad. Publ. (Dordrecht, 2001), pp. 853-968. http://dx.doi.org/10.1007/978-94-017-0470-0_3

S. G. Matthews, Partial metric topology, in: Proc. 8th Summer Conference on General Topology and Applications. Ann. New York Acad. Sci. 728 (1994), 183-197. http://dx.doi.org/10.1111/j.1749-6632.1994.tb44144.x

S. Oltra, S. Romaguera, E.A. Sánchez-Pérez, Bicompleting weightable quasi-metric spaces and partial metric spaces, Rend. Circolo Mat. Palermo, 50 (2002), 151-162. http://dx.doi.org/10.1007/BF02871458

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

S. J. O’Neill, Partial metrics, valuations and domain theory, in: Proc. 11th Summer Conference on General Topology and Applications. Ann. New York Acad. Sci. 806 (1996), 304-315. http://dx.doi.org/10.1111/j.1749-6632.1996.tb49177.x

E. Rakotch, A note on contractive mappings, Proc. Amer. Math. Soc. 13 (1962), 459-465. http://dx.doi.org/10.1090/S0002-9939-1962-0148046-1

S. Reich, Kannan’s fixed point thorem, Boll. U. M. I. 4 (1971), 1-11.

S. Romaguera, M. Schellekens, Weightable qusi-metric semigroups and semilattices, In: Proc. MFCSIT2000, Electronic Notes in Theoretical Computer Science 40 (2003), 12 pages.

S. Romaguera, M. Schellekens, Partial metric monoids and semivaluation spaces, Topology Appl., to appear.

M. Schellekens, A characterization of partial metrizability: domains are quantifiable, Theoret. Comput. Sci. 305 (2003), 409-432. http://dx.doi.org/10.1016/S0304-3975(02)00705-3

M. Schellekens, The correpondence between partial metrics and semivaluations, Theoret. Comput. Sci. 315 (2004), 135-149. http://dx.doi.org/10.1016/j.tcs.2003.11.016

A. K. Seda, Quasi-metrics and fixed point in computing, Bull. EATCS 60 (1996), 154-163.

P. Waszkierwicz, Quantitative continuous domains, Appl. Categor. Struct. 11 (2003),41-67. http://dx.doi.org/10.1023/A:1023012924892

P. Waszkierwicz, The local triangle axiom in topology and domain theory, Appl. Gen. Topology 4 (2003), 47-70.

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