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TOEPLITZ DETERMINANTS WHOSE ELEMENTS ARE THE COEFFICIENTS OF ANALYTIC AND UNIVALENT FUNCTIONS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 97 / Issue 2 / April 2018
- Published online by Cambridge University Press:
- 26 February 2018, pp. 253-264
- Print publication:
- April 2018
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- Article
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- You have access
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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.
