<abstract xmlns="http://www.w3.org/1999/xhtml">

Let <italic>S</italic> denote the class of functions f which are analytic and univalent in the unit disk 𝔻 = {z : |z| &lt; 1} and normalized with <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausm-2023-0017_eq_001.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mtext>f</mtext><mrow><mo>(</mo><mtext>z</mtext><mo>)</mo></mrow><mo>=</mo><mtext>z</mtext><mo>+</mo><msubsup><mo>∑</mo><mrow><mtext>n</mtext><mo>=</mo><mn>2</mn></mrow><mo>∞</mo></msubsup><mrow><msub><mrow><mi>α</mi></mrow><mtext>n</mtext></msub><msup><mrow><mtext>z</mtext></mrow><mtext>n</mtext></msup></mrow></mrow></math>
<tex-math>{\rm{f}}\left( {\rm{z}} \right) = {\rm{z}} + \sum\nolimits_{{\rm{n = 2}}}^\infty {{\alpha _{\rm{n}}}{{\rm{z}}^{\rm{n}}}}</tex-math>
</alternatives>
</inline-formula>. Using a method based on Grusky coefficients we study two problems over the class <italic>S</italic>: estimate of the fourth logarithmic coefficient and upper bound of the coefficient difference |α5| − |α4|.
</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+∑n=2∞αnzn
{\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|.

Two applications of Grunsky coefficients in the theory of univalent functions

Department of Mathematics, Faculty of Civil Engineering

Department of Mathematics and Informatics, Faculty of Mechanical Engineering

Ss. Cyril and Methodius University in Skopje

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Two applications of Grunsky coefficients in the theory of univalent functions"}

Let S denote the class of functions f which are analytic and univalent in the unit disk 𝔻 = {z : |z| < 1} and normalized with...

Two applications of Grunsky coefficients in the theory of univalent functions

Published Online: Dec 26, 2023

Page range: 304 - 313

Received: Jan 19, 2022

DOI: https://doi.org/10.2478/ausm-2023-0017

Keywords
univalent functions, Grunsky coefficients, fourth logarithmic coefficient, coefficient difference

© 2023 Milutin Obradović et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Two applications of Grunsky coefficients in the theory of univalent functions

Published Online: Dec 26, 2023

Page range: 304 - 313

Received: Jan 19, 2022

DOI: https://doi.org/10.2478/ausm-2023-0017

Keywordsunivalent functions, Grunsky coefficients, fourth logarithmic coefficient, coefficient difference

© 2023 Milutin Obradović et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
univalent functions, Grunsky coefficients, fourth logarithmic coefficient, coefficient difference