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ON THE DIFFERENCE OF COEFFICIENTS OF OZAKI CLOSE-TO-CONVEX FUNCTIONS

Part of: Geometric function theory

Published online by Cambridge University Press:  18 June 2020

YOUNG JAE SIM Open the ORCID record for YOUNG JAE SIM [Opens in a new window]  and
DEREK K. THOMAS Open the ORCID record for DEREK K. THOMAS [Opens in a new window]
YOUNG JAE SIM
Affiliation:
Department of Mathematics,Kyungsung University, Busan48434, Korea email yjsim@ks.ac.kr
DEREK K. THOMAS*
Affiliation:
Department of Mathematics,Swansea University, Bay Campus,Swansea, SA1 8EN, UK email d.k.thomas@swansea.ac.uk
*
✉d.k.thomas@swansea.ac.uk
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Abstract

Let $f$ be analytic in the unit disk $\mathbb{D}=\{z\in \mathbb{C}:|z|<1\}$ and ${\mathcal{S}}$ be the subclass of normalised univalent functions given by $f(z)=z+\sum _{n=2}^{\infty }a_{n}z^{n}$ for $z\in \mathbb{D}$. We give sharp upper and lower bounds for $|a_{3}|-|a_{2}|$ and other related functionals for the subclass ${\mathcal{F}}_{O}(\unicode[STIX]{x1D706})$ of Ozaki close-to-convex functions.

Keywords

univalent functionOzaki close-to-convex functiondifference of coefficients

MSC classification

Primary: 30C50: Coefficient problems for univalent and multivalent functions
Secondary: 30C55: General theory of univalent and multivalent functions 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 103 , Issue 1 , February 2021 , pp. 124 - 131
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

The first author was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean Government (MSIP, Ministry of Science, ICT and Future Planning) (No. NRF-2017R1C1B5076778).

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