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This article is cited in 1 scientific paper (total in 1 paper)
Third Hankel determinant for the inverse of reciprocal of bounded turning functions has a positive real part of order alpha
B. Venkateswarlua, N. Ranib a Department of Mathematics,
GST, GITAM University,
Benguluru Rural Dist-562 163,
Karnataka, India
b Department of Sciences and Humanities,
Praveenya Institute of Marine Engineering and Maritime studies,
Modavalasa- 534 002, Visakhapatnam, A. P., India
Abstract:
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.
Received: 29.06.2016
Citation:
B. Venkateswarlu, N. Rani, “Third Hankel determinant for the inverse of reciprocal of bounded turning functions has a positive real part of order alpha”, Ufimsk. Mat. Zh., 9:2 (2017), 112–121; Ufa Math. J., 9:2 (2017), 109–118
Linking options:
https://www.mathnet.ru/eng/ufa379https://doi.org/10.13108/2017-9-2-109 https://www.mathnet.ru/eng/ufa/v9/i2/p112
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Abstract page: | 217 | Russian version PDF: | 86 | English version PDF: | 10 | References: | 35 |
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