caa a22 4500 463177932 CHVBK 20180406164830.0 cr unu---uuuuu 170326e20070801xx s 000 0 eng 10.1007/s11139-006-9002-8 doi (NATIONALLICENCE)springer-10.1007/s11139-006-9002-8 Koumandos Stamatis Department of Mathematics and Statistics, The University of Cyprus, P.O. Box 20537, 1678, Nicosia, Cyprus aut An extension of Vietoris's inequalities [Elektronische Daten] [Stamatis Koumandos] We establish a best possible extension of a famous Theorem of Vietoris about the positivity of a general class of cosine sums. Our result refines and sharpens several earlier generalizations of this Theorem, and settles some open questions regarding the possibility of further improvement of it. Some new inequalities for trigonometric sums are given. We show that our results have applications within the context of positive sums of Gegenbauer polynomials and quadrature methods. We also obtain some existing estimates for the location of zeros of certain trigonometric polynomials under a weakened condition on their coefficients. Springer Science + Business Media, LLC, 2006 Positive trigonometric sums nationallicence Trigonometric polynomials nationallicence Inequalities nationallicence Zeros nationallicence Positive sums of Gegenbauer polynomials nationallicence Quadrature nationallicence The Ramanujan Journal Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 14/1(2007-08-01), 1-38 1382-4090 14:1<1 2007 14 11139 https://doi.org/10.1007/s11139-006-9002-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11139-006-9002-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Koumandos Stamatis Department of Mathematics and Statistics, The University of Cyprus, P.O. Box 20537, 1678, Nicosia, Cyprus aut NATIONALLICENCE 773 0- The Ramanujan Journal Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 14/1(2007-08-01), 1-38 1382-4090 14:1<1 2007 14 11139 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer