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A fixed point theorem for generalized contractions. (English) Zbl 1286.54044

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
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