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Abstract

In this paper we give estimates of the differences $|γ_3|-|γ_2|$ and $|γ_4|-|γ_3|$ for the class of functions $f$ univalent in the unit disc and normalized by $f(0)=f'(0)-1=0$. Here, $γ_{2}$, $γ_{3}$ and $γ_{4}$ are the initial logarithmic coefficients of the function $f$.

Results & Lemmas (1)

Each result is auto-extracted from the paper via OCR - the math is shown verbatim and may carry occasional transcription artifacts. Click to expand the full statement.

Theorem 1 Theorem 1. Let, and be the logarithmic coefficients of function. Then and.
Theorem 1. Let $\gamma_2$ , $\gamma_3$ and $\gamma_4$ be the logarithmic coefficients of function $f \in \mathcal{S}$ . Then $$|\gamma_3| - |\gamma_2| \le \frac{1}{\sqrt{5}}$$ and $|\gamma_4| - |\gamma_3| \le \frac{1}{\sqrt{7}}$ .

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