V $-Moreau envelope of nonconvex functions on smooth Banach spaces

We continue the study of the properties of the $ V $-Moreau envelope and generalized $ (f, \lambda) $-projection that we started in [<xref ref-type="bibr" rid="b5">5 ] . In this paper, we study the differentiability and the regularity of the $ V $-Moreau envelope and the Hö...

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Bibliographic Details
Published in:	AIMS mathematics Vol. 9; no. 10; pp. 28589 - 28610
Main Author:	Bounkhel, Messaoud
Format:	Journal Article
Language:	English
Published:	AIMS Press 01.01.2024
Subjects:	generalized $ (f lambda) $-projection p $-uniformly convex banach spaces q $-uniformly smooth banach spaces uniformly generalized prox-regular sets v $-moreau envelope v $-prox-regular functions
ISSN:	2473-6988, 2473-6988
Online Access:	Get full text
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Summary:	We continue the study of the properties of the $ V $-Moreau envelope and generalized $ (f, \lambda) $-projection that we started in [<xref ref-type="bibr" rid="b5">5 ] . In this paper, we study the differentiability and the regularity of the $ V $-Moreau envelope and the Hölder continuity of the generalized $ (f, \lambda) $-projection. Our results extend many existing results from the convex case to the nonconvex case and from Hilbert spaces to Banach spaces. Even on Hilbert spaces and for convex functions and sets, we derived new results.
ISSN:	2473-6988 2473-6988
DOI:	10.3934/math.20241387