Comptes Rendus
Analyse et géométrie complexes
On the Fekete–Szegö type functionals for functions which are convex in the direction of the imaginary axis
Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1213-1226.

In this paper we consider two functionals of the Fekete–Szegö type: Φ f (μ)=a 2 a 4 -μa 3 2 and Θ f (μ)=a 4 -μa 2 a 3 for analytic functions f(z)=z+a 2 z 2 +a 3 z 3 +..., zΔ, (Δ={z:|z|<1}) and for real numbers μ. For f which is univalent and convex in the direction of the imaginary axis, we find sharp bounds of the functionals Φ f (μ) and Θ f (μ). It is possible to transfer the results onto the class 𝒦 (i) of functions convex in the direction of the imaginary axis with real coefficients as well as onto the class 𝒯 of typically real functions. As corollaries, we obtain bounds of the second Hankel determinant in 𝒦 (i) and 𝒯.

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DOI : 10.5802/crmath.144
Classification : 30C50

Paweł Zaprawa 1

1 Lublin University of Technology, Department of Mathematics, Faculty of Mechanical Engineering, Nadbystrzycka 38D, 20-618, Lublin, Poland
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Paweł Zaprawa. On the Fekete–Szegö type functionals for functions which are convex in the direction of the imaginary axis. Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1213-1226. doi : 10.5802/crmath.144. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.144/

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