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A refinement of Vietoris' inequality for sine polynomials
Author(s) -
Alzer Horst,
Koumandos Stamatis,
Lamprecht Martin
Publication year - 2010
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200810029
Subject(s) - mathematics , image (mathematics) , inequality , sine , pure mathematics , mathematical analysis , discrete mathematics , geometry , computer vision , computer science
LetwhereIn 1958, Vietoris proved that σ n ( x ) is positive for all n ≥ 1 and x ∈ (0, π ). We establish the following refinement. The inequalitieshold for all natural numbers n and real numbers n ≥ 1 and x ∈ (0, π ) if and only if
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