Journal of Convex Analysis 13 (2006), No. 3, 477--488
Copyright Heldermann Verlag 2006
Variational Methods in Classical Open Mapping Theorems
Dominique Azé
UMR CNRS MIP, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse, France
aze@mip.ups-tlse.fr
Jean-Noël Corvellec
Laboratoire MANO, Université de Perpignan, 52 Avenue Paul Alduy, 66860 Perpignan, France
corvellec@univ-perp.fr
We describe some basic facts from the theory of linear error bounds for lower semicontinuous functions on complete metric spaces, relying upon Ekeland's variational principle and on the notion of strong slope. We then show how this variational method yields the classical Banach-Schauder and Lusternik-Graves open mapping theorems.
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