Third Hankel determinant for the inverse of reciprocal of bounded turning functions has a positive real part of order alpha
Ufa mathematical journal, Tome 9 (2017) no. 2, pp. 109-118
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Let $RT$ be the class of functions $f(z)$ univalent in the unit disk $E = {z : |z| 1}$ such that $\mathrm{Re}\, f'(z) > 0$, $z\in E$, and $H_3(1)$ be the third Hankel determinant for inverse function to $f(z)$. In this paper we obtain, first an upper bound for the second Hankel determinant, $|t_2 t_3 - t_4|$, and the best possible upper bound for the third Hankel determinant $H3(1)$
for the functions in the class of inverse of reciprocal of bounded turning functions having a positive real part of order alpha.
Keywords:
univalent function, function whose reciprocal derivative has a positive real part, third Hankel determinant, positive real function, Toeplitz determinants.
@article{UFA_2017_9_2_a8,
author = {B. Venkateswarlu and N. Rani},
title = {Third {Hankel} determinant for the inverse of reciprocal of bounded turning functions has a positive real part of order alpha},
journal = {Ufa mathematical journal},
pages = {109--118},
publisher = {mathdoc},
volume = {9},
number = {2},
year = {2017},
language = {en},
url = {http://geodesic.mathdoc.fr/item/UFA_2017_9_2_a8/}
}
TY - JOUR AU - B. Venkateswarlu AU - N. Rani TI - Third Hankel determinant for the inverse of reciprocal of bounded turning functions has a positive real part of order alpha JO - Ufa mathematical journal PY - 2017 SP - 109 EP - 118 VL - 9 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/UFA_2017_9_2_a8/ LA - en ID - UFA_2017_9_2_a8 ER -
%0 Journal Article %A B. Venkateswarlu %A N. Rani %T Third Hankel determinant for the inverse of reciprocal of bounded turning functions has a positive real part of order alpha %J Ufa mathematical journal %D 2017 %P 109-118 %V 9 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/UFA_2017_9_2_a8/ %G en %F UFA_2017_9_2_a8
B. Venkateswarlu; N. Rani. Third Hankel determinant for the inverse of reciprocal of bounded turning functions has a positive real part of order alpha. Ufa mathematical journal, Tome 9 (2017) no. 2, pp. 109-118. http://geodesic.mathdoc.fr/item/UFA_2017_9_2_a8/