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Fixed point theorems for contractive mappings in complete $$G$$-metric spaces. (English) Zbl 1179.54067
The paper provides some fixed point theorems for contractive-type maps on complete $$G$$-metric spaces in the sense of these authors [J. Nonlinear Convex Anal. 7, No. 2, 286–297 (2006; Zbl 1111.54025)]. The fixed points are unique and are continuity points of those contractive maps.

##### MSC:
 54H25 Fixed-point and coincidence theorems (topological aspects)
##### Keywords:
$$G$$-metric space; fixed point
Full Text:
##### References:
 [1] Gähler, S, 2-metrische Räume und ihre topologische struktur, Mathematische Nachrichten, 26, 115-148, (1963) · Zbl 0117.16003 [2] Gähler, S, Zur geometric [inlineequation not available: see fulltext.]-metriche räume, Revue Roumaine de Mathématiques Pures et Appliquées, 11, 665-667, (1966) · Zbl 0158.20402 [3] Dhage, BC, Generalised metric spaces and mappings with fixed point, Bulletin of the Calcutta Mathematical Society, 84, 329-336, (1992) · Zbl 0782.54037 [4] Dhage, BC, Generalized metric spaces and topological structure. I, Analele Ştiinţifice ale Universităţii Al. I. Cuza din Iaşi. Serie Nouă. Matematică, 46, 3-24, (2000) · Zbl 0995.54020 [5] Ha, KS; Cho, YJ; White, A, Strictly convex and strictly 2-convex 2-normed spaces, Mathematica Japonica, 33, 375-384, (1988) · Zbl 0651.46030 [6] Mustafa Z, Sims B: Some remarks concerning -metric spaces.Proceedings of the International Conference on Fixed Point Theory and Applications, July 2004, Valencia, Spain 189-198. · Zbl 1079.54017 [7] Mustafa, Z; Sims, B, A new approach to generalized metric spaces, Journal of Nonlinear and Convex Analysis, 7, 289-297, (2006) · Zbl 1111.54025 [8] Mustafa Z: A new structure for generalized metric spaces—with applications to fixed point theory, Ph.D. thesis. The University of Newcastle, Callaghan, Australia; 2005.
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