Article
On regularization in superreflexive Banach spaces by infimal convolution formulas
Author/s | Cepedello Boiso, Manuel |
Department | Universidad de Sevilla. Departamento de Análisis Matemático |
Publication Date | 1998 |
Deposit Date | 2016-07-12 |
Published in |
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Abstract | We present here a new method for approximating functions defined on
superreflexive Banach spaces by differentiable functions with α-H¨older derivatives (for some 0 < α ≤ 1). The smooth approximation is given by means of ... We present here a new method for approximating functions defined on superreflexive Banach spaces by differentiable functions with α-H¨older 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 ∆-convex C1,α functions converging uniformly on bounded sets to f 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. |
Funding agencies | Ministerio de Educación y Ciencia (MEC). España |
Citation | Cepedello Boiso, M. (1998). On regularization in superreflexive Banach spaces by infimal convolution formulas. Studia Mathematica, 129 (3), 265-284. |
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