Geodesic
On regularization in superreflexive Banach spaces by infimal convolution formulas
Studia Mathematica, Tome 129 (1998) no. 3, pp. 265-284

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We present here a new method for approximating functions defined on superreflexive Banach spaces by differentiable functions with α-Hölder derivatives (for some 0 α≤ 1). The smooth approximation is given by means of an explicit formula enjoying good properties from the minimization point of view. For instance, for any function f which is bounded below and uniformly continuous on bounded sets this formula gives a sequence of Δ-convex $C^{1,α}$ functions converging to f uniformly on bounded sets and preserving the infimum and the set of minimizers of f. The techniques we develop are based on the use of extended inf-convolution formulas and convexity properties such as the preservation of smoothness for the convex envelope of certain differentiable functions.
DOI : 10.4064/sm-129-3-265-284
Keywords: regularization in Banach spaces, convex functions

Manuel Cepedello-Boiso 1

1 
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Manuel Cepedello-Boiso. On regularization in superreflexive Banach spaces by infimal convolution formulas. Studia Mathematica, Tome 129 (1998) no. 3, pp. 265-284. doi: 10.4064/sm-129-3-265-284

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