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SECOND HANKEL DETERMINANT OF LOGARITHMIC COEFFICIENTS OF CONVEX AND STARLIKE FUNCTIONS

Part of: Geometric function theory

Published online by Cambridge University Press:  30 September 2021

BOGUMIŁA KOWALCZYK Open the ORCID record for BOGUMIŁA KOWALCZYK [Opens in a new window]  and
ADAM LECKO Open the ORCID record for ADAM LECKO [Opens in a new window]
BOGUMIŁA KOWALCZYK
Affiliation:
Department of Complex Analysis, Faculty of Mathematics and Computer Science, University of Warmia and Mazury in Olsztyn, ul. Słoneczna 54, 10-710 Olsztyn, Poland e-mail: [email protected]
ADAM LECKO*
Affiliation:
Department of Complex Analysis, Faculty of Mathematics and Computer Science, University of Warmia and Mazury in Olsztyn, ul. Słoneczna 54, 10-710 Olsztyn, Poland
*
e-mail: [email protected]
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Abstract

We begin the study of Hankel matrices whose entries are logarithmic coefficients of univalent functions and give sharp bounds for the second Hankel determinant of logarithmic coefficients of convex and starlike functions.

Keywords

starlike functionconvex functionCarathéodory functionHankel determinantlogarithmic coefficient

MSC classification

Primary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 105 , Issue 3 , June 2022 , pp. 458 - 467
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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