Fekete-Szeg\"o problem for certain subclasses of univalent functions
Bull. Korean Math. Soc. 2015 Vol. 52, No. 6, 1937-1943
Published online November 30, 2015
Allu Vasudevarao
Indian Institute of Technology Khargpur
Abstract : For $1\leq\alpha<2$, let $\mathcal{F}(\alpha)$ denote the class of locally univalent normalized analytic functions $f(z)=z+\sum_{n=2}^{\infty} a_n z^n$ in the unit disk $\mathbb{D}=\{z\in\mathbb{C}:\, |z|<1\}$ satisfying the condition $${\rm Re}\left(1+\frac{zf''(z)}{f'(z)}\right)>\frac{\alpha}{2}-1. $$ In the present paper, we shall obtain the sharp upper bound for Fekete-Szeg\"o functional $|a_3-\lambda a_2^2|$ for the complex parameter $\lambda$.
Keywords : univalent functions, starlike, convex, close-to-convex and Fekete-Szeg\"o problem
MSC numbers : Primary 30C45
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