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Ufa Mathematical Journal, 2017, Volume 9, Issue 2, Pages 109–118
DOI: https://doi.org/10.13108/2017-9-2-109
(Mi ufa379)
 

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
References:
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
Russian version:
Ufimskii Matematicheskii Zhurnal, 2017, Volume 9, Issue 2, Pages 112–121
Bibliographic databases:
Document Type: Article
MSC: 30C45; 30C50
Language: English
Original paper language: English
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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\paper Third Hankel determinant for the inverse of reciprocal of bounded turning functions has a positive real part of order alpha
\jour Ufimsk. Mat. Zh.
\yr 2017
\vol 9
\issue 2
\pages 112--121
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\jour Ufa Math. J.
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\pages 109--118
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  • https://www.mathnet.ru/eng/ufa379
  • https://doi.org/10.13108/2017-9-2-109
  • https://www.mathnet.ru/eng/ufa/v9/i2/p112
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Уфимский математический журнал
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    English version PDF:10
    References:35
     
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