The generalized Minkowski functional with applications in approximation theory

Revesz, SGy; Sarantopoulos, Y

dc.contributor.author	Revesz, SGy	en
dc.contributor.author	Sarantopoulos, Y	en
dc.date.accessioned	2014-03-01T01:21:37Z
dc.date.available	2014-03-01T01:21:37Z
dc.date.issued	2004	en
dc.identifier.issn	0944-6532	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16275
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-4544268293&partnerID=40&md5=ae476b6b2050501283ef7c8f4ac52a25	en
dc.subject	Central symmetrization	en
dc.subject	Centroid	en
dc.subject	Cone of convex bodies	en
dc.subject	Convex body	en
dc.subject	Convex functions in normed spaces	en
dc.subject	Halfspaces and layers	en
dc.subject	Lipschitz bounds	en
dc.subject	Measure of symmetry	en
dc.subject	Minkowski functional	en
dc.subject	Support function	en
dc.subject	Supporting hyperplanes	en
dc.subject	Width of K in a direction	en
dc.subject.classification	Mathematics	en
dc.subject.other	CONVEX-BODIES	en
dc.subject.other	MULTIVARIATE POLYNOMIALS	en
dc.subject.other	BANACH-SPACES	en
dc.subject.other	INEQUALITIES	en
dc.subject.other	BERNSTEIN	en
dc.subject.other	MARKOV	en
dc.subject.other	ANALOGS	en
dc.title	The generalized Minkowski functional with applications in approximation theory	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	2004	en
heal.abstract	We give a systematic and thorough study of geometric notions and results connected to Minkowski's measure of symmetry and the extension of the well-known Minkowski functional to arbitrary, not necessarily symmetric convex bodies K on any (real) normed space X. Although many of the notions and results we treat in this paper can be found elsewhere in the literature, they are scattered and possibly hard to find. Further, we are not aware of a systematic study of this kind and we feel that several features, connections and properties - e.g. the connections between many equivalent formulations - are new, more general and they are put in a better perspective now. In particular, we prove a number of fundamental properties of the extended Minkowski functional alpha(K, x), including convexity, global Lipschitz boundedness, linear growth and approximation of the classical Minkowski functional of the central symmetrization of the body K. Our aim is to present how in the recent years these notions proved to be surprisingly relevant and effective in problems of approximation theory.	en
heal.publisher	HELDERMANN VERLAG	en
heal.journalName	Journal of Convex Analysis	en
dc.identifier.isi	ISI:000224032300004	en
dc.identifier.volume	11	en
dc.identifier.issue	2	en
dc.identifier.spage	303	en
dc.identifier.epage	334	en