Some application of Grunsky coefficients in the theory of univalent functions

Milutin Obradović; Nikola Tuneski

doi:10.2478/aupcsm-2025-0005

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Some application of Grunsky coefficients in the theory of univalent functions

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Volume 25 (2025): Issue 1 (December 2025)

By: Milutin Obradović and Nikola Tuneski

Open Access

|Nov 2025

Abstract

Let function f be normalized, analytic and univalent in the unit disk 𝔻 = {z : |z| < 1} and $f (z) = z + \sum_{n = 2}^{\infty} a_{n} z^{n}$ f\left( z \right) = z + \sum\nolimits_{n = 2}^\infty {{a_n}{z^n}} . Using a method based on Grusky coefficients we study several problems over that class of univalent functions: upper bounds of the special case of the generalized Zalcman conjecture |a₂a₃ − a₄|, of the third logarithmic coefficient, and of the second Hankel determinant for the logarithmic coefficients.

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Articles in this issue

DOI: https://doi.org/10.2478/aupcsm-2025-0005 | Journal eISSN: 2300-133X | Journal ISSN: 2081-545X

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Language: English

Page range: 23 - 30

Submitted on: Jun 19, 2025

Accepted on: Jun 19, 2025

Published on: Nov 26, 2025

Published by: Pedagogical University of Cracow

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

Sunivalent functions,

Grunsky coefficients,

third logarithmic coefficient,

coefficient difference,

generalised Zalcman conjecture,

second Hankel determinant,

third Hankel determinant

Related subjects:

Mathematics,

General mathematics

© 2025 Milutin Obradović, Nikola Tuneski, published by Pedagogical University of Cracow
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 License.

Volume 25 (2025): Issue 1 (December 2025)