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A best proximity point theorem for generalized weakly contractive non self mappings. (English) Zbl 1311.41022

Classical results in fixed point theory, like Banach contraction principle, deal with the existence of fixed points for mappings of (complete) metric spaces. In case when a map \(T : X \to X\) of a metric space \((X,d)\) has no fixed point, a possible replacement is to find best proximity points, that are elements \(x\in X\) such that \(d(x,Tx)\) is a minimum.
In this paper the authors provide criteria for the existence of unique best proximity points for some generalized weakly contractive mappings in the context of complete metric spaces.

MSC:

41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
47H10 Fixed-point theorems
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