1997 | OriginalPaper | Buchkapitel
Fixed Points for Nonexpansive Mappings and Normal Structure
verfasst von : J. M. Ayerbe Toledano, T. Domínguez Benavides, G. López Acedo
Erschienen in: Measures of Noncompactness in Metric Fixed Point Theory
Verlag: Birkhäuser Basel
Enthalten in: Professional Book Archive
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The most known and important metric fixed point theorem is the Banach fixed point theorem, also called the contractive mapping principle, which assures that every contraction from a complete metric space into itself has a unique fixed point. We recall that a mapping T from a metric space (X, d) into itself is said to be a contraction if there exists k ∈ [0,1) such that d(Tx, Ty) ≤ kd(x, y) for every x, y ∈ X. This theorem appeared in explicit form in Banach’s Thesis in 1922 [Bn] where it was used to establish the existence of a solution for an integral equation. The simplicity of its proof and the possibility of attaining the fixed point by using successive approximations have made this theorem a very useful tool in Analysis and in Applied Mathematics.