On uniformly convex functions

Raja Baño, Matías; Grelier, Guillaume Guy Marcel

Publication:
On uniformly convex functions

dc.contributor.author	Raja Baño, Matías
dc.contributor.author	Grelier, Guillaume Guy Marcel
dc.contributor.department	Matemáticas
dc.date.accessioned	2024-02-20T08:02:12Z
dc.date.available	2024-02-20T08:02:12Z
dc.date.issued	2022
dc.description	Acceso restringido
dc.description.abstract	Non-convex functions that yet satisfy a condition of uniform convexity for non-close points can arise in discrete constructions. We prove that this sort of discrete uniform convexity is inherited by the convex envelope, which is the key to obtain other remarkable properties such as the coercivity. Our techniques allow to retrieve Enflo’s uniformly convex renorming of super-reflexive Banach spaces as the regularization of a raw function built from trees. Among other applications, we provide a sharp estimation of the distance of a given function to the set of differences of Lipschitz convex functions. Finally, we prove the equivalence of several possible ways to quantify the super weakly noncompactness of a convex subset of a Banach space.	es
dc.format	application/pdf	es
dc.format.extent	25	es
dc.identifier.citation	Journal of Mathematical Analysis and Applications 505 (2022) 125442
dc.identifier.doi	https://doi.org/10.1016/j.jmaa.2021.125442
dc.identifier.issn	Print: 0022-247X
dc.identifier.issn	Electronic: 1096-0813
dc.identifier.uri	http://hdl.handle.net/10201/139541
dc.language	eng	es
dc.publisher	Elsevier
dc.relation	This research has been supported by the Grants of Ministerio de Economía, Industria y Competitividad MTM2017-83262-C2-2-P; and Fundación Séneca Región de Murcia 20906/PI/18.	es
dc.rights	info:eu-repo/semantics/openAccess	es
dc.subject	Uniform convexity	en
dc.subject	Super weak compactness	en
dc.subject.other	CDU::5 - Ciencias puras y naturales::51 - Matemáticas::517 - Análisis	es
dc.title	On uniformly convex functions	es
dc.type	info:eu-repo/semantics/article	es
dspace.entity.type	Publication	es