zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
Existence of fixed point results in $G$-metric spaces. (English) Zbl 1179.54066
Summary: The purpose of this paper is to prove the existence of fixed points of contractive mappings defined on $G$-metric space where the completeness is replaced with weaker conditions. Moreover, we show that these conditions do not guarantee the completeness of $G$-metric spaces.

MSC:
54H25Fixed-point and coincidence theorems in topological spaces
WorldCat.org
Full Text: DOI EuDML
References:
[1] S. Gähler, “2-metrische Räume und ihre topologische Struktur,” Mathematische Nachrichten, vol. 26, pp. 115-148, 1963. · Zbl 0117.16003 · doi:10.1002/mana.19630260109
[2] S. Gähler, “Zur geometric 2-metriche raume,” Revue Roumaine de Mathématiques Pures et Appliquées, vol. 11, pp. 664-669, 1966.
[3] B. C. Dhage, “Generalized metric space and mapping with fixed point,” Bulletin of the Calcutta Mathematical Society, vol. 84, pp. 329-336, 1992. · Zbl 0782.54037
[4] B. C. Dhage, “Generalized metric spaces and topological structure-I,” Analele \cStiin\ctifice ale Universit\uatii Al. I. Cuza din Ia\csi, vol. 46, no. 1, pp. 3-24, 2000. · Zbl 0995.54020
[5] B. C. Dhage, “On generalized metric spaces and topological structure-II,” Pure and Applied Mathematika Sciences, vol. 40, no. 1-2, pp. 37-41, 1994. · Zbl 0869.54031
[6] K. S. Ha, Y. J. Cho, and A. White, “Strictly convex and strictly 2-convex 2-normed spaces,” Mathematica Japonica, vol. 33, no. 3, pp. 375-384, 1988. · Zbl 0651.46030
[7] S. V. R. Naidu, K. P. R. Rao, and N. Srinivasa Rao, “On the concepts of balls in a D-metric space,” International Journal of Mathematics and Mathematical Sciences, no. 1, pp. 133-141, 2005. · Zbl 1083.54526 · doi:10.1155/IJMMS.2005.133 · eudml:52198
[8] Z. Mustafa and B. Sims, “Some remarks concerning D-metric spaces,” in Proceedings of the International Conference on Fixed Point Theory and Applications, pp. 189-198, Valencia, Spain, July 2003. · Zbl 1079.54017
[9] Z. Mustafa and B. Sims, “A new approach to generalized metric spaces,” Journal of Nonlinear and Convex Analysis, vol. 7, no. 2, pp. 289-297, 2006. · Zbl 1111.54025
[10] Z. Mustafa, H. Obiedat, and F. Awawdeh, “Some fixed point theorem for mapping on complete G-metric spaces,” Fixed Point Theory and Applications, vol. 2008, Article ID 189870, 12 pages, 2008. · Zbl 1148.54336 · doi:10.1155/2008/189870 · eudml:54664