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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, Number 7, Pages 67–80
DOI: https://doi.org/10.26907/0021-3446-2021-7-67-80 (Mi ivm9696) 		 
On Hadamard compositions of Gelfond–Leont'ev derivatives of analytic functions

M. N. Sheremetaa, O. M. Mulyavab

a Ivan Franko National University of Lviv, 1 Universytetska str., Lviv, 79000 Ukraine
b Kyiv National University of Food Technologies, 68 Volodymyrska str., Kyiv, 01033 Ukraine
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DOI: https://doi.org/10.26907/0021-3446-2021-7-67-80
Abstract: For analytic functions $f$ and $g$ given by power series with different finite convergence radii, properties of the Hadamard composition of their Gelfond–Leont'ev derivatives is investigated. For study, generalized orders are used. The connection between the growth of the maximal term of the Hadamard composition of Gelfond–Leont'ev derivatives and the growth of the maximal term of the Gelfond–Leont'ev derivative of Hadamard composition is established. Similar results is obtained in terms of the classical order and lower order of growth.
Keywords: analytic function, Hadamard composition, Gelfond–Leont'ev derivative, maximal term.
Received: 18.07.2020
Revised: 03.09.2020
Accepted: 01.10.2020
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2021, Volume 65, Issue 7, Pages 58–70
DOI: https://doi.org/10.3103/S1066369X21070070
Document Type: Article
UDC: 517.53
Language: Russian
Citation: M. N. Sheremeta, O. M. Mulyava, “On Hadamard compositions of Gelfond–Leont'ev derivatives of analytic functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, no. 7, 67–80; Russian Math. (Iz. VUZ), 65:7 (2021), 58–70
Citation in format AMSBIB
\Bibitem{SheMul21}
\by M.~N.~Sheremeta, O.~M.~Mulyava
\paper On Hadamard compositions of Gelfond--Leont'ev derivatives of analytic functions
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2021
\issue 7
\pages 67--80
\mathnet{http://mi.mathnet.ru/ivm9696}
\crossref{https://doi.org/10.26907/0021-3446-2021-7-67-80}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2021
\vol 65
\issue 7
\pages 58--70
\crossref{https://doi.org/10.3103/S1066369X21070070}
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