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- W1657426348 abstract "We present here a new method for approximating functions defined on superreflexive Banach spaces by differentiable functions with $alpha$-Holder derivatives (for some $0<alphaleq 1$). 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 $Delta$-convex ${Cal{C}}^{1,alpha}$ 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 {sl extended inf-convolution} formulas and convexity properties such as the preservation of smoothness for the convex envelope of certain differentiable functions." @default.
- W1657426348 created "2016-06-24" @default.
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- W1657426348 date "1997-06-12" @default.
- W1657426348 modified "2023-09-27" @default.
- W1657426348 title "On regularization in superreflexive Banach spaces by infimal convolution formulas" @default.
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