Envelopes for sets and functions II: generalized polarity and conjugacy

Abstract : 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.
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Submitted on : Tuesday, January 29, 2019 - 9:16:58 AM
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Alexandre Cabot, Abderrahim Jourani, Lionel Thibault. Envelopes for sets and functions II: generalized polarity and conjugacy. Journal of Nonlinear and Convex Analysis, Yokohama, 2018, 19 (8), pp.1297-1318. ⟨http://www.ybook.co.jp/online2/jncav19-8.html⟩. ⟨hal-01997447⟩



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