Browsing by Subject "Trigonometric polynomials"

Now showing items 1-4 of 4

    • Article  

      An extension of Vietoris's inequalities 

      Koumandos, S. (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 ...
    • Article  

      Inequalities for two sine polynomials 

      Alzer, H.; Koumandos, S. (2006)
      We prove: (I) For all integers n ≥ 2 and real numbers x ∈ (0, π) we have (Formula Presented) with the best possible constant bounds (Formula Presented) (II) The inequality (Formula Presented) holds for all even integers n ...
    • Article  

      A new refinement of Young's inequality 

      Alzer, H.; Koumandos, S. (2007)
      A classical theorem due to Young states that the cosine polynomial c n(x) = 1 + ∑k=1n cos(kx)/k is positive for all n ≥ 1 and x ∈ (0, π). We prove the following refinement. For all n ≥ 2 and x ∈ [0, π] we have 1/6 + c(π - ...
    • Article  

      On the partial sums of a fourier series 

      Alzer, H.; Koumandos, S. (2008)
      We give sharp lower estimates for the partial sums of the Fourier series sin x + cos2x/2 + sin 3x/3 + cos 4x/4 + ..., with both an even and odd number of terms. Our results are obtained through a monotonicity property of ...