Abstract
In this paper we give sharp bounds of the difference of the moduli of the second and the first logarithmic coefficient for Bazilevič class of univalent functions.
Results & Lemmas (1)
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Theorem 1
Theorem 1. Let for some. Then The right estimation is sharp for all, while the left is sharp for, where and are the positive roots of the…
Theorem 1. Let $f \in \mathcal{B}_1(\alpha)$ for some $\alpha > 0$ . Then
$$-\frac{1}{\sqrt{(\alpha+1)^2+1}} \le |\gamma_2| - |\gamma_1| \le \frac{1}{\alpha+2}.$$
The right estimation is sharp for all $\alpha > 0$ , while the left is sharp for $\alpha_1 \le \alpha \le \alpha_2$ , where $\alpha_1 = \frac{1}{2} \left( \sqrt{6} - 2 \right) = 0.2247 \dots$ and $\alpha_2 = \sqrt{2} - 1 = 0.4142 \dots$ are the positive roots of the equation
$$2\alpha^4 + 8\alpha^3 + 5\alpha^2 - 6\alpha + 1 = 0.$$
Function classes studied:
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