Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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CERTAIN PROPERTIES OF THE CLASS OF UNIVALENT FUNCTIONS WITH REAL COEFFICIENTS

  • Milutin Obradovic (Department of Mathematics Faculty of Civil Engineering University of Belgrade) ;
  • Nikola Tuneski (Department of Mathematics and Informatics Faculty of Mechanical Engineering Ss. Cyril and Methodius University in Skopje)
  • Received : 2022.09.19
  • Accepted : 2023.04.21
  • Published : 2023.09.30
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Abstract

Let 𝓤+ be the class of analytic functions f such that ${\frac{z}{f(z)}}$ has real and positive coefficients and f-1 be its inverse. In this paper we give sharp estimates of the initial coefficients and initial logarithmic coefficients for f, as well as, sharp estimates of the second and the third Hankel determinant for f and f-1. We also show that the Zalcman conjecture holds for functions f from 𝓤+.

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References

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