🧭 New here?
Take a guided tour of the site.
← Back to Papers

On the difference of initial logarithmic coefficients for the class of univalent functions

Milutin Obradovic, Nikola Tuneski · 2023 📄 arXiv →

Continue from this paper

Indexing is not verification. Extracted statements should be checked against the source.

Read the original paper ↗ Search this title Learn what Atlas can verify → Suggest a correction or ask a question →
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 $|\gamma_4| - |\gamma_3| \le \frac{1}{\sqrt{7}}$ .

Related Papers

Simple proofs of certain inequalities with logarithmic coefficients of univalent
2023
On the difference of coefficients of univalent functions
2020
Hankel determinant for a class of analytic functions
2019
Hankel determinant of second order for some classes of analytic functions
2019
New upper bounds of the third Hankel determinant for some classes of univalent f
2019
↑↓ navigate↵ openesc closeall results
✦ 291 explorers have wandered the registry - thanks for stopping by. Tell us what you'd like to see →
Usage & privacy

We use first-party site metrics to improve navigation: page visits, internal clicks, search result counts (not search terms), and approximate active time. A random tab ID groups events for seven days; GPC/DNT turns this off. The separate visitor count uses a self-hosted pseudonymous fingerprint and also respects GPC/DNT.

💬 Feedback