On regularization in superreflexive Banach spaces by infimal convolution formulas
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 v...
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 1998 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/43525 |
| Acceso en línea: | http://hdl.handle.net/11441/43525 |
| Access Level: | acceso abierto |
| Palabra clave: | Regularization in Banach spaces Convex functions |
| Sumario: | 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. |
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