×

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:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E50 Complete metric spaces
PDFBibTeX XMLCite
Full Text: DOI