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THE THIRD HERMITIAN-TOEPLITZ AND HANKEL DETERMINANTS FOR PARABOLIC STARLIKE FUNCTIONS

Sushil Kumar|Vaithiyanathan Ravichandran|Rosihan M. Ali
대한수학회 (The Korean Mathematical Society)|2023.03|대한수학회보 (Bulletin of the KMS)|제60권 제2호|pp. 281-291|DOI 10.4134/BKMS.b210368

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참고문헌

키워드

subordinationHankel determinantuniformly convex functionsHermitian-Toeplitz determinantParabolic starlike functions
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초록

A normalized analytic function $f$ is parabolic starlike if $w(z)$ $:=zf'(z)/f(z)$ maps the unit disk into the parabolic region $\{w: \operatorname{Re} w>|w-1|\}$. Sharp estimates on the third Hermitian-Toeplitz determinant are obtained for parabolic starlike functions. In addition, upper bounds on the third Hankel determinants are also determined.

Abstract

A normalized analytic function $f$ is parabolic starlike if $w(z)$ $:=zf'(z)/f(z)$ maps the unit disk into the parabolic region $\{w: \operatorname{Re} w>|w-1|\}$. Sharp estimates on the third Hermitian-Toeplitz determinant are obtained for parabolic starlike functions. In addition, upper bounds on the third Hankel determinants are also determined.

참고문헌 (26)

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