A duality for starshaped functions

• Autorzy: Penot J.-P.
• Języki publikacji: EN

Abstrakty

EN

A conjugacy is introduced for the class of starshaped functions from [0, infinity] into [0, infinity], i.e. the class of functions f such that their slope s : t --> f (t)/t is nondecreasing. This class is stable by several operations and plays a key role in the study of uniformly convex and uniformly smooth convex functions and in the geometry of Banach spaces. Here the inversion of the subdifferential as in the Legendre-Fenchel transform is replaced by an inversion device of the slope s which uses the ordering of R.

Słowa kluczowe

EN

conjugacy; conjugate function; duality; Frenchel transform; quasi-inverse; slope; starshaped

PL

dwoistość; funkcja sprzężona; nachylenie; przekształcenie Frenchela; sprzężenie

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2002
• Tom: Vol. 50, no 2
• Strony: 127--139
• Opis fizyczny: Bibliogr. 31 poz.

Twórcy

autor

Penot J.-P.

• Université de Pau et des Pays de L’adour, Laboratoire de Mathématiques Appliquées, Ura 2055 - CNRS, Avenue de L’université, 64000 Pau - France

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