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

Abstract : 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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Journal articles
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https://hal.archives-ouvertes.fr/hal-01666630
Contributor : Abderrahim Jourani <>
Submitted on : Monday, December 18, 2017 - 3:46:00 PM
Last modification on : Tuesday, May 28, 2019 - 1:54:03 PM

### Identifiers

• HAL Id : hal-01666630, version 1

### Citation

Alexandre Cabot, Abderrahim Jourani, Lionel Thibault, Dariusz Zagrodny. The attainment set of $\varphi$-envelope and genericity properties. Mathematica Scandinavica, 2017. ⟨hal-01666630⟩

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