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A fixed point theorem of Reich in G-metric spaces. (English) Zbl 1220.54030
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:
54H25Fixed-point and coincidence theorems in topological spaces
54E50Complete metric spaces