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

Author(s):

Milutin Obradovic , Nikola Tuneski *

Message:
Article Type:
Research/Original Article (بدون رتبه معتبر)
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 $f(z)=z+\sum_{n=2}^{\infty} a_n z^n$. If additionally, \[ \left| \left(\frac{z}{f(z)}\right)^2 f'(z) -1\right|<\lambda \quad\quad (z\in D), \]then $f$ belongs to the class $U(\lambda)$, $0<\lambda\le1$. In this paper we prove sharp upper bound of the modulus of the fifth coefficient of $f$ from $U(\lambda)$ in the case when $0.400436\ldots \le\lambda\le1$.
Keywords:

Univalent functions , Class U($ , lambda$) , fifth coefficient , sharp estimate

Language:
English
Published:
Caspian Journal of Mathematical Sciences, Volume:11 Issue: 2, Summer Autumn 2022
Pages:
410 to 416
https://www.magiran.com/p2535276