Browsing by Subject "Positive trigonometric sums"
Now showing items 1-6 of 6
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An extension of Vietoris's inequalities
(2007)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 ...
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Inequalities for trigonometric sums
(2012)We give a survey of recent results on positive trigonometric sums. Farreaching extensions and generalizations of classical results are presented. We provide new proofs as well as additional remarks and comments. We also ...
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On a conjecture for trigonometric sums and starlike functions
(2007)We pose and discuss the following conjecture: let snμ (z) {colon equals} ∑k = 0n frac((μ)k, k !) zk, and for ρ ∈ (0, 1] let μ* (ρ) be the unique solution μ ∈ (0, 1] of ∫0(ρ + 1) π sin fenced(t - ρ π) tμ - 1 dt = 0 .Then ...
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On a conjecture for trigonometric sums and starlike functions, II
(2010)We prove the case ρ=1/4 of the following conjecture of Koumandos and Ruscheweyh: let snμ(z)=Σk=0n(μ)k/ k!zk, and for ρε(0,1] let μ≤(ρ) be the unique solution of 0(ρ+1)πsin(t-ρπ)tμ-1dt =0 in (0,1]. Then we have pipearg[(1 ...
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Article
On a monotonic trigonometric sum
(1997)By establishing a cosine analogue of a result of Askey and Steinig on a monotonic sine sum, this paper sharpens and unifies several results associated with Young's inequality for the partial sums of Σk-1 cos kθ.
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Remarks on a sine polynomial
(2009)Let n ≥ 0 be an integer. Then we have for x ε (0, π) : ∑k=0 n(2n+1 n-k)sin((2k+1)x)/2k+1 ≤ 8 n-rfnet-temp!/(2n+1)!! The upper bound is best possible. This complements a result of Fejér, who proved that the sine polynomial ...