# On regularization in superreflexive Banach spaces by infimal convolution formulas

Studia Mathematica (1998)

- Volume: 129, Issue: 3, page 265-284
- ISSN: 0039-3223

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topCepedello-Boiso, Manuel. "On regularization in superreflexive Banach spaces by infimal convolution formulas." Studia Mathematica 129.3 (1998): 265-284. <http://eudml.org/doc/216504>.

@article{Cepedello1998,

abstract = {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.},

author = {Cepedello-Boiso, Manuel},

journal = {Studia Mathematica},

keywords = {regularization in Banach spaces; convex functions; approximating functions; superreflexive Banach spaces; -Hölder derivatives; extended inf-convolution formulas},

language = {eng},

number = {3},

pages = {265-284},

title = {On regularization in superreflexive Banach spaces by infimal convolution formulas},

url = {http://eudml.org/doc/216504},

volume = {129},

year = {1998},

}

TY - JOUR

AU - Cepedello-Boiso, Manuel

TI - On regularization in superreflexive Banach spaces by infimal convolution formulas

JO - Studia Mathematica

PY - 1998

VL - 129

IS - 3

SP - 265

EP - 284

AB - 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.

LA - eng

KW - regularization in Banach spaces; convex functions; approximating functions; superreflexive Banach spaces; -Hölder derivatives; extended inf-convolution formulas

UR - http://eudml.org/doc/216504

ER -

## References

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