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Some notes on fixed points of quasi-contraction maps. (English) Zbl 1206.54061

A self map T:XX such that for some λ(0,1) and for every x,yX there exists


such that


is said to be a quasi-contraction. It is proved that every quasi-contraction defined on a complete cone metric space has a unique fixed point. Moreover, every quasi-contraction defined on a cone metric space possesses the property (P), that is F(T)=F(T n ) for all n1, where F(T) denotes the set of all fixed points of the mapping T:XX.

54H25Fixed-point and coincidence theorems in topological spaces
54E35Metric spaces, metrizability
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