Karakostas, George L. A fixed point theorem for generalized contractions. (English) Zbl 1286.54044 Bull. Greek Math. Soc. 50, 27-32 (2005). Summary: We push further the idea of A. Branciari [Int. J. Math. Math. Sci. 29, No. 9, 531–536 (2002; Zbl 0993.54040)] and show the existence of unique fixed points for mappings defined on complete metric spaces \((X,d)\) which behave like contractions through a positive function \(G\). We call them generalized contractions. Our results extend the results of [loc. cit.] as well as the classical ones concerning contractive mappings. MSC: 54H25 Fixed-point and coincidence theorems (topological aspects) 47H10 Fixed-point theorems Citations:Zbl 0993.54040 PDFBibTeX XMLCite \textit{G. L. Karakostas}, Bull. Greek Math. Soc. 50, 27--32 (2005; Zbl 1286.54044)