Geodesic
Zalcman and generalized Zalcman conjecture for a subclass of univalent functions
Novi Sad Journal of Mathematics, Tome 52 (2022) no. 1.

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The function $f(z)=z+\sum_{n=2}^{\infty} a_n z^n$, normalized, analytic and univalent in the unit disk ${\mathbb D}=\{z:|z|1\}$, belongs to the class $\mathcal{U}$ if, and only if, \[ \left| \left(\frac{z}{f(z)}\right)^2 f'(z) -1\right|1 \quad\quad (z\in{\mathbb D}). \] In this paper we prove the Zalcman and the generalized Zalcman conjecture for the class $\mathcal{U}$ and some values of parameters in the conjectures.
Publié le :
DOI : 10.30755/NSJOM.12436
Classification : 30C45, 30C50, 30C55
Keywords: univalent functions, class ${\mathcal{U}}$, Zalcman conjecture, generalized Zalcman conjecture 
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     title = {Zalcman and generalized {Zalcman} conjecture for a subclass of univalent functions},
     journal = {Novi Sad Journal of Mathematics},
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Milutin Obradović; Nikola Tuneski. Zalcman and generalized Zalcman conjecture for a subclass of univalent functions. Novi Sad Journal of Mathematics, Tome 52 (2022) no. 1. doi : 10.30755/NSJOM.12436. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.12436/

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