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Ufimsk. Mat. Zh., 2017, Volume 9, Issue 2, Pages 112–121 (Mi ufa379)  

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.

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English version:
Ufa Mathematical Journal, 2017, 9:2, 109–118 (PDF, 330 kB); https://doi.org/10.13108/2017-9-2-109

Bibliographic databases:

MSC: 30C45; 30C50
Received: 29.06.2016
Language:

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

Citation in format AMSBIB
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\vol 9
\issue 2
\pages 112--121
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\pages 109--118
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