6533b853fe1ef96bd12abef4
RESEARCH PRODUCT
Envelopes for sets and functions II: generalized polarity and conjugacy
Alexandre CabotAbderrahim JouraniLionel Thibaultsubject
regularizationconvexityLegendre-Fenchel conjugateMutually generating conjugacy functionsΦ-envelopeΓ- polarMutually generating polarity sets.MSC: 52A41 49J53 41A65[MATH] Mathematics [math][MATH]Mathematics [math]Generalized conjugacydescription
International audience; Let X,Y be two nonempty sets, Φ an extended real-valued bivariate coupling function on X × Y and Γ a subset of X × Y. The present paper provides extensions to the well-known generalized Φ-conjugacy and Γ-polarity of diverse results of our previous work [2] related to φ-conjucacy and Λ-polarity, where Λ is a subset of a vector space E and φ is a function on E defining the particular coupling function (x,y)→φ(x−y) on E × E. A particular attention is devoted to the conjugacy functions (resp. polarity sets) which are mutually generating. Finally, for a superadditive conjugacy function Φ, we obtain a full description of the class of Φ-envelopes.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-01-01 |