Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On the Fekete-Szegö Problem for Starlike Functions of Complex Order

  • Darwish, Hanan (Department of Mathematics, Faculty of Science, Mansoura University) ;
  • Lashin, Abdel-Moniem (Department of Mathematics, Faculty of Science, Mansoura University) ;
  • Al Saeedi, Bashar (Department of Mathematics, Faculty of Science & Engineering, Manchester Metropolitan University)
  • Received : 2016.01.28
  • Accepted : 2020.05.04
  • Published : 2020.09.30
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Abstract

For a non-zero complex number b and for m and n in 𝒩0 = {0, 1, 2, …} let Ψn,m(b) denote the class of normalized univalent functions f satisfying the condition ${\Re}\;\[1+{\frac{1}{b}}\(\frac{D^{n+m}f(z)}{D^nf(z)}-1\)\]\;>\;0$ in the unit disk U, where Dn f(z) denotes the Salagean operator of f. Sharp bounds for the Fekete-Szegö functional |a3 - 𝜇a22| are obtained.

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References

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