On a conjecture for trigonometric sums and starlike functions, II

  • Authors:

  • Stamatis Koumandos;Martin Lamprecht

  • Affiliations:

  • Department of Mathematics and Statistics, The University of Cyprus, P. O. Box 20537, 1678 Nicosia, Cyprus;Department of Mathematics and Statistics, The University of Cyprus, P. O. Box 20537, 1678 Nicosia, Cyprus

  • Venue:
  • Journal of Approximation Theory
  • Year:
  • 2010

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Abstract

We prove the case @r=14 of the following conjecture of Koumandos and Ruscheweyh: let s"n^@m(z)@?@?"k"="0^n(@m)"kk!z^k, and for @r@?(0,1] let @m^*(@r) be the unique solution of @!"0^(^@r^+^1^)^@psin(t-@r@p)t^@m^-^1dt=0 in (0,1]. Then we have |arg[(1-z)^@rs"n^@m(z)]|@?@r@p/2 for 0