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Matematicheskie Zametki, 2019, Volume 105, Issue 4, paper published in the English version journal (Mi mzm11718)  
Papers published in the English version of the journal

Third-Order Hankel Determinant for Transforms of the Reciprocal of Bounded Turning Functions

D. Vamshee Krishnaa, T. RamReddyb, D. Shalinic

a Department of Mathematics, GITAM University, Visakhapatnam-530 045, A. P., India
b Department of Mathematics, Kakatiya University, Warangal-506 009, T. S., India
c Department of Mathematics, Dr. B. R. Ambedkar University, Srikakulam-532 410, A. P., India
Abstract: In this paper, we make an attempt to introduce a new subclass of analytic functions. Using the Toeplitz determinants, we obtain the best possible upper bound for the third-order Hankel determinant associated with the $k^{th}$ root transform $[f(z^{k})]^{{1}/{k}}$ of the normalized analytic function $f(z)$ when it belongs to this class, defined on the open unit disc in the complex plane.
Keywords: analytic function, upper bound, reciprocal of a bounded turning function, third Hankel functional, positive real function, Toeplitz determinants.
Received: 09.06.2017
Revised: 18.10.2018
English version:
Mathematical Notes, 2019, Volume 105, Issue 4, Pages 535–542
DOI: https://doi.org/10.1134/S000143461903026X
Bibliographic databases:
Document Type: Article
Language: English
Citation: D. Vamshee Krishna, T. RamReddy, D. Shalini, “Third-Order Hankel Determinant for Transforms of the Reciprocal of Bounded Turning Functions”, Math. Notes, 105:4 (2019), 535–542
Citation in format AMSBIB
\Bibitem{VamRamSha19}
\by D.~Vamshee Krishna, T.~RamReddy, D.~Shalini
\paper Third-Order Hankel Determinant for Transforms
of the Reciprocal of Bounded Turning Functions
\jour Math. Notes
\yr 2019
\vol 105
\issue 4
\pages 535--542
\mathnet{http://mi.mathnet.ru/mzm11718}
\crossref{https://doi.org/10.1134/S000143461903026X}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3954797}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85065643476}
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