Browsing Τμήμα Μαθηματικών και Στατιστικής / Department of Mathematics and Statistics by Subject "Inequalities"

Now showing items 1-9 of 9

    • 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  

      On a conjecture for trigonometric sums and starlike functions, II 

      Koumandos, S.; Lamprecht, M. (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 ...
    • Article  

      On a conjecture of Clark and Ismail 

      Alzer, H.; Berg, C.; Koumandos, S. (2005)
      Let Φm (x) = -xmψ(m) (x), where ψ denotes the logarithmic derivative of Euler's gamma function. Clark and Ismail prove in a recently published article that if m ∈ {1,2,..., 16}, then Φm(m) is completely monotonic on (0, ...
    • Article  

      On a conjectured inequality of Gautschi and Leopardi for Jacobi polynomials 

      Koumandos, S. (2007)
      Motivated by work on positive cubature formulae over the spherical surface, Gautschi and Leopardi conjectured that the inequality (equation presented) holds for α, β > - 1 and n ≥ 1, θ∈ ∈(0, π), where Pn(α,β)(x) are the ...
    • Article  

      On a trigonometric sum of Vinogradov 

      Alzer, H.; Koumandos, S. (2004)
      The trigonometric sum f(m, n) = ∑ k=1 m-1 sin(πkn/m) /sin(πk/m) (1 < m ∈ N, n ∈ N) has several applications in number theory. We prove that the mean value inequalities c1m(log m + γ - logπ/2) ≤ 1/m ∑ n=1 f(m, n) < c2m(log ...
    • 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 ...
    • Article  

      A sharp bound for a sine polynomial 

      Alzer, H.; Koumandos, S. (2003)
      We prove that (Formula Presented) for all integers n ≥ 1 and real numbers x. The upper bound Si(π) is best possible. This result refines inequalities due to Fejér (1910) and Lenz (1951). © 2003, Instytut Matematyczny. All ...
    • Article  

      A Sharp Inequality for a Trigonometric Sum 

      Alzer, H.; Koumandos, S. (2013)
      We prove that the inequality, holds for all natural numbers n and real numbers x with x ∈ [0, Π]. The sign of equality is valid if and only if n = 1 and x = π /2. © 2012 Springer Basel AG.