A refinement of Vietoris' inequality for sine polynomials |
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| Authors: | Horst Alzer Stamatis Koumandos Martin Lamprecht |
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| Affiliation: | 1. Morsbacher Str. 10, 51545 Waldbr?l, Germany;2. Department of Mathematics and Statistics, The University of Cyprus, P. O. Box 20537, 1678 Nicosia, Cyprus |
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| Abstract: | Let ![equation image]( "equation image") where ![equation image]( "equation image") In 1958, Vietoris proved that σn (x) is positive for all n ≥ 1 and x ∈ (0, π). We establish the following refinement. The inequalities ![equation image]( "equation image") hold for all natural numbers n and real numbers n ≥ 1 and x ∈ (0, π) if and only if ![equation image]( "equation image") |
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| Keywords: | Vietoris inequality sine polynomials |
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