Browsing Τμήμα Μαθηματικών και Στατιστικής / Department of Mathematics and Statistics by Author "Ruscheweyh, S."

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    • Article  

      On a conjecture for trigonometric sums and starlike functions 

      Koumandos, S.; Ruscheweyh, S. (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 ...
    • Article  

      Positive Gegenbauer polynomial sums and applications to starlike functions 

      Koumandos, S.; Ruscheweyh, S. (2006)
      Let sn(f,z):=∑k=0n akz k be the nth partial sum of f(z)= ∑k=0 ∞ akzk. We show that Re s n(f/z,z)>0 holds for all z ∈ D, n ∈ N, and all starlike functions f of order λ iff λ0 ≤ λ 0 for all n ∈ N, x ∈ [-1,1], and 0 < μ ≤ ...