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Article Dans Une Revue Mathematica Scandinavica Année : 2019

The attainment set of $\varphi$-envelope and genericity properties

Résumé

The attainment set of the $\varphi-$envelope of a function at a given point is investigated. The inclusion of the attainment set of the $\varphi$-envelope of the closed convex hull of a function into the attainment set of the function is preserved in sufficiently general settings toencompass the case $\varphi $ being a norm in a power not less than $1$. The nonemptiness of the attainment set is guaranteed on genericsubsets of a given space, in several fundamental cases.
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Dates et versions

hal-01666630 , version 1 (18-12-2017)

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Alexandre Cabot, Abderrahim Jourani, Lionel Thibault, Dariusz Zagrodny. The attainment set of $\varphi$-envelope and genericity properties. Mathematica Scandinavica, 2019, 124 (2), pp.203-246. ⟨10.7146/math.scand.a-110766⟩. ⟨hal-01666630⟩
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