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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.

54H25 Fixed-point and coincidence theorems (topological aspects)
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[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
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