Two applications of Grunsky coefficients in the theory of univalent functions

Milutin Obradović; Nikola Tuneski

doi:10.2478/ausm-2023-0017

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Two applications of Grunsky coefficients in the theory of univalent functions

Acta Universitatis Sapientiae, Mathematica

Volume 15 (2023): Issue 2 (December 2023)

By: Milutin Obradović and Nikola Tuneski

Open Access

|Dec 2023

Abstract

Let S denote the class of functions f which are analytic and univalent in the unit disk 𝔻 = {z : |z| < 1} and normalized with $f (z) = z + \sum_{n = 2}^{\infty} α_{n} z^{n}$ {\rm{f}}\left( {\rm{z}} \right) = {\rm{z}} + \sum\nolimits_{{\rm{n = 2}}}^\infty {{\alpha _{\rm{n}}}{{\rm{z}}^{\rm{n}}}} . Using a method based on Grusky coefficients we study two problems over the class S: estimate of the fourth logarithmic coefficient and upper bound of the coefficient difference |α₅| − |α₄|.

References

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Articles in this issue

DOI: https://doi.org/10.2478/ausm-2023-0017 | Journal eISSN: 2066-7752

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Language: English

Page range: 304 - 313

Submitted on: Jan 19, 2022

Published on: Dec 26, 2023

Published by: Sapientia Hungarian University of Transylvania

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

univalent functions,

Grunsky coefficients,

fourth logarithmic coefficient,

coefficient difference

Related subjects:

Mathematics,

General mathematics

© 2023 Milutin Obradović, Nikola Tuneski, published by Sapientia Hungarian University of Transylvania
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 15 (2023): Issue 2 (December 2023)