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Journal Articles Journal of Functional Analysis Year : 2001

A Non-Convex Analogue to Fenchel Duality

Mohammed Bachir
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Abstract

We introduce and study a new notion of conjugacy, similar to Fenchel conjugacy, in a non-convex setting. Dual versions of Šmulyan's classical result are established in the framework of this conjugacy, which reveal a relation between well-posed problems and the differentiability. As an application we deduce the generic Fréchet differentiability of the norm $‖·‖∞$ in certain spaces of bounded continuous functions (i.e., $Lipα(X) $ for $0<α \leq 1$).
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Dates and versions

hal-01183279 , version 1 (07-08-2015)

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  • HAL Id : hal-01183279 , version 1

Cite

Mohammed Bachir. A Non-Convex Analogue to Fenchel Duality. Journal of Functional Analysis, 2001, 181 (2), pp.300-312. ⟨hal-01183279⟩
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