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TOEPLITZ DETERMINANTS WHOSE ELEMENTS ARE THE COEFFICIENTS OF ANALYTIC AND UNIVALENT FUNCTIONS

Part of: Geometric function theory

Published online by Cambridge University Press:  26 February 2018

MD FIROZ ALI ,
D. K. THOMAS  and
A. VASUDEVARAO
MD FIROZ ALI
Affiliation:
Indian Statistical Institute, Chennai Centre, 37, Nelson Manickam Road, Aminjikarai, Chennai-600 029, Tamilnadu, India email [email protected]
D. K. THOMAS
Affiliation:
Department of Mathematics, Swansea University, Singleton Park, Swansea, SA2 8PP, UK email [email protected]
A. VASUDEVARAO*
Affiliation:
Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur-721 302, West Bengal, India email [email protected]
*
✉[email protected]
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Abstract

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Let ${\mathcal{S}}$ denote the class of analytic and univalent functions in $\mathbb{D}:=\{z\in \mathbb{C}:|z|<1\}$ which are of the form $f(z)=z+\sum _{n=2}^{\infty }a_{n}z^{n}$. We determine sharp estimates for the Toeplitz determinants whose elements are the Taylor coefficients of functions in ${\mathcal{S}}$ and certain of its subclasses. We also discuss similar problems for typically real functions.

Keywords

analytic functionunivalent functionstarlike functionconvex functionclose-to-convex functiontypically real functionToeplitz determinant

MSC classification

Primary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
Secondary: 30C55: General theory of univalent and multivalent functions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 97 , Issue 2 , April 2018 , pp. 253 - 264
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

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