Sharp estimate of the fifth coefficients for the class U(lambda)

Document Type : Research Articles

Authors

1 Department of Mathematics, Faculty of Civil Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, 11000, Belgrade, Serbia

2 Department of Mathematics and Informatics, Faculty of Mechanical Engineering, Ss. Cyril and Methodius University in Skopje, Karpos II b.b., 1000 Skopje, Republic of North Macedonia

Abstract

Let f be function that is analytic in the unit disk D={z:|z|<1}, normalized such that f(0)=f′(0)−1=0, i.e., of type f(z)=z+∑n=2∞anzn. If additionally, |(zf(z))2f′(z)−1|<λ(z∈D),
then f belongs to the class U(λ), 0<λ≤1. In this paper we prove sharp upper bound of the modulus of the fifth coefficient of f from U(λ) in the case when 0.400436…≤λ≤1.

Keywords

Caspian Journal of Mathematical Sciences
Volume 11, Issue 2
2022
Pages 410-416

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