An application of the Krein-Milman theorem to Bernstein and Markov inequalities

Munoz-Fernandez, GA; Sarantopoulos, Y; Seoane-Sepulveda, JB

dc.contributor.author	Munoz-Fernandez, GA	en
dc.contributor.author	Sarantopoulos, Y	en
dc.contributor.author	Seoane-Sepulveda, JB	en
dc.date.accessioned	2014-03-01T01:27:52Z
dc.date.available	2014-03-01T01:27:52Z
dc.date.issued	2008	en
dc.identifier.issn	0944-6532	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/18616
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-45849118354&partnerID=40&md5=badcf018c2e66bba6186a69762f229d2	en
dc.subject.classification	Mathematics	en
dc.title	An application of the Krein-Milman theorem to Bernstein and Markov inequalities	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	2008	en
heal.abstract	Given a trinomial of the form p(x) = ax(m) + bx(n) + c with a, b, c is an element of R, we obtain, explicitly, the best possible constant M.,,(x) in the inequality vertical bar p'(x)vertical bar <= M-m,M-n(x).parallel to p parallel to, where x is an element of [-1, 1] is fixed and parallel to p parallel to is the sup norm of p over [-1, 1]. This answers a question to an old problem, first studied by Markov, for a large family of trinomials. We obtain the mappings M-m,M-n(x) by means of classical convex analysis techniques, in particular, using the Krein-Milman approach.	en
heal.publisher	HELDERMANN VERLAG	en
heal.journalName	Journal of Convex Analysis	en
dc.identifier.isi	ISI:000257342300008	en
dc.identifier.volume	15	en
dc.identifier.issue	2	en
dc.identifier.spage	299	en
dc.identifier.epage	312	en