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Matematicheskie Zametki, 2019, Volume 105, Issue 4, paper published in the English version journal
(Mi mzm11718)
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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
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
Linking options:
https://www.mathnet.ru/eng/mzm11718
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