zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Suzuki’s type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces. (English) Zbl 1241.54035
The following two abstract and a little artificial notions are studied: (i) partial metric spaces; (ii) $0$-complete metric spaces. Then some formal generalizations of the Banach contraction theorem for mappings in such spaces are obtained. Moreover, a coincidence result is proved.

54H25Fixed-point and coincidence theorems in topological spaces
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
Full Text: DOI
[1] Altun, I.; Durmaz, G.: Some fixed point theorems on ordered cone metric spaces, Rend. circ. Mat. Palermo 58, 319-325 (2009) · Zbl 1184.54038 · doi:10.1007/s12215-009-0026-y
[2] Haghi, R. H.; Rezapour, Sh.; Shahzad, N.: Some fixed point generalizations are not real generalizations, Nonlinear anal. 74, 1799-1803 (2011) · Zbl 1251.54045
[3] Kirk, W. A.: Caristi’s fixed point theorem and metric convexity, Colloq. math. 36, 81-86 (1976) · Zbl 0353.53041
[4] Matthews, S. G.: Partial metric topology, Ann. New York acad. Sci. 728, 183-197 (1994) · Zbl 0911.54025
[5] Nieto, J. J.; Rodríguez-López, R.: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22, 223-239 (2005) · Zbl 1095.47013 · doi:10.1007/s11083-005-9018-5
[6] O’neill, S. J.: Partial metrics, valuations and domain theory, Ann. New York acad. Sci. 806, 304-315 (1996) · Zbl 0889.54018
[7] Oltra, S.; Valero, O.: Banach’s fixed point theorem for partial metric spaces, Rend. istit. Mat. univ. Trieste 36, 17-26 (2004) · Zbl 1080.54030
[8] Ran, A. C. M.; Reurings, M. C.: A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. amer. Math. soc. 132, 1435-1443 (2004) · Zbl 1060.47056 · doi:10.1090/S0002-9939-03-07220-4
[9] Romaguera, S.: A kirk type characterization of completeness for partial metric spaces, Fixed point theory appl. 2010 (2010) · Zbl 1193.54047 · doi:10.1155/2010/493298
[10] Suzuki, T.: A generalized Banach contraction principle that characterizes metric completeness, Proc. amer. Math. soc. 136, 1861-1869 (2008) · Zbl 1145.54026 · doi:10.1090/S0002-9939-07-09055-7
[11] Valero, O.: On Banach fixed point theorems for partial metric spaces, Appl. gen. Topol. 6, 229-240 (2005) · Zbl 1087.54020