# zbMATH — the first resource for mathematics

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:
 54H25 Fixed-point and coincidence theorems (topological aspects)
Full Text:
##### 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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.