Almeida, Angel; Harjani, Jackie; Sadarangani, Kishin A best proximity point theorem for generalized weakly contractive non self mappings. (English) Zbl 1311.41022 J. Convex Anal. 21, No. 4, 989-1006 (2014). 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. Reviewer: Cătălin Badea (Villeneuve d’Ascq) MSC: 41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) 47H10 Fixed-point theorems Keywords:best proximity point; generalized weakly contractive mapping; fixed point PDFBibTeX XMLCite \textit{A. Almeida} et al., J. Convex Anal. 21, No. 4, 989--1006 (2014; Zbl 1311.41022) Full Text: Link