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Zbl 1220.54030
Mustafa, Zead; Obiedat, Hamed
A fixed point theorem of Reich in $G$-metric spaces. (English)
[J] Cubo 12, No. 1, 83-93 (2010). ISSN 0716-7776

Summary: In this paper we prove some fixed point results for mappings satisfying sufficient contractive conditions on a complete $G$-metric space; we also show that if the $G$-metric space $(X,G)$ is symmetric, then the existence and uniqueness of these fixed points follows from Reich's theorem in an ordinary metric space $(X,d_G)$, where $(X,d_G)$ is the metric induced by the $G$-metric space $(X,G)$.

MSC 2000:: *54H25 Fixed-point theorems in topological spaces
54E50 Complete metric spaces

Keywords: metric space; generalized metric space; $D$-metric space; 2-metric space

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