Upper bounds of Toeplitz determinants for a subclass of alpha-close-to-convex functions

Jha, Anand Kumar and Sahoo, Pravati

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creative_2022_31_1_81_90

DOI: https://doi.org/10.37193/CMI.2022.01.08

Issue no: Vol 31/2022 no. 1 Tags: convex function, Starlike function, Hankel determinant, close-to-convex function, Toeplitz determinant

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Let $\mathcal{A}$ be the class of analytic functions in the unit disc ${\mathbb U}$ which are of the form $f(z)=z+\sum_{n=2}^{\infty}a_nz^n$ . For $0\leq\alpha< 1$ , let ${\mathcal C}_\alpha$ , be the class of all functions $f \in \mathcal{A}$ satisfying the condition $\rm{Re}\{f'(z)+\alpha zf''(z)\}>0$ . We consider the Toeplitz matrices whose elements are the coefficients $a_n$ of the function $f$ in the class ${\mathcal C}_\alpha$ . In this paper we obtain upper bounds for the Toeplitz determinants.