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 Vladikavkaz. Mat. Zh., 2020, Volume 22, Number 1, Pages 43–48 (Mi vmj713)

Hankel determinant of third kind for certain subclass of multivalent analytic functions

D. Vamshee Krishnaa, D. Shalinib

a GITAM Institute of Science, Visakhapatnam 530045, Andhra Pradesh, India
b Dr. B. R. Ambedkar University, Srikakulam 532410, Andhra Pradesh, India

Abstract: The objective of this paper is to obtain an upper bound (not sharp) to the third order Hankel determinant for certain subclass of multivalent ($p$-valent) analytic functions, defined in the open unit disc $E$. Using the Toeplitz determinants, we may estimate the Hankel determinant of third kind for the normalized multivalent analytic functions belongng to this subclass. But, using the technique adopted by Zaprawa [1], i. e., grouping the suitable terms in order to apply Lemmas due to Hayami [2], Livingston [3] and Pommerenke [4], we observe that, the bound estimated by the method adopted by Zaprawa is more refined than using upon applying the Toeplitz determinants.

Key words: $p$-valent analytic function, upper bound, third Hankel determinant, positive real function.

DOI: https://doi.org/10.23671/VNC.2020.1.57538

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UDC: 512.643.86+517.546
MSC: 30C45, 30C50
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Citation: D. Vamshee Krishna, D. Shalini, “Hankel determinant of third kind for certain subclass of multivalent analytic functions”, Vladikavkaz. Mat. Zh., 22:1 (2020), 43–48

Citation in format AMSBIB
\Bibitem{VamSha20} \by D.~Vamshee~Krishna, D.~Shalini \paper Hankel determinant of third kind for certain subclass of multivalent analytic functions \jour Vladikavkaz. Mat. Zh. \yr 2020 \vol 22 \issue 1 \pages 43--48 \mathnet{http://mi.mathnet.ru/vmj713} \crossref{https://doi.org/10.23671/VNC.2020.1.57538} 

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