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Sibirskii Matematicheskii Zhurnal, 2022, Volume 63, Number 1, Pages 167–179
DOI: https://doi.org/10.33048/smzh.2022.63.111 (Mi smj7648) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Extremal problems of Bernstein-type and an operator preserving inequalities between polynomials

G. V. Milovanovichab, A. Mirc, A. Hussainc

a Faculty of Sciences and Mathematics, University of Niš, Niš, Serbia
b The Serbian Academy of Sciences and Arts, Belgrade, Serbia
c Department of Mathematics, University of Kashmir, Srinagar, 190006, India
Full-text PDF (299 kB) Citations (8)
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DOI: https://doi.org/10.33048/smzh.2022.63.111
Abstract: Under consideration are the well-known extremal problems of Bernstein-type which relate the uniform norm between polynomials on the unit disk in the plane. We establish a few new inequalities in both directions for the generalized $\mathcal{B}_n$-operator while accounting for the placement of the zeros of the underlying polynomials. Also, we obtain various estimates for the maximum modulus of a polynomial as well as some inequalities of Erdös–Lax type.
Keywords: polynomial, inequalities in the complex domain, zeros, $N$-operator.
Funding agency Grant number
Serbian Academy of Sciences and Arts 96
The first author was partly supported by the Serbian Academy of Sciences and Arts (Project \( \Phi \)-96).
Received: 05.02.2021
Revised: 06.06.2021
Accepted: 11.10.2021
English version:
Siberian Mathematical Journal, 2022, Volume 63, Issue 1, Pages 138–148
DOI: https://doi.org/10.1134/S0037446622010116
Bibliographic databases:
Document Type: Article
UDC: 517.538
Language: Russian
Citation: G. V. Milovanovich, A. Mir, A. Hussain, “Extremal problems of Bernstein-type and an operator preserving inequalities between polynomials”, Sibirsk. Mat. Zh., 63:1 (2022), 167–179; Siberian Math. J., 63:1 (2022), 138–148
Citation in format AMSBIB
\Bibitem{MilMirHus22}
\by G.~V.~Milovanovich, A.~Mir, A.~Hussain
\paper Extremal problems of Bernstein-type and an operator preserving inequalities between polynomials
\jour Sibirsk. Mat. Zh.
\yr 2022
\vol 63
\issue 1
\pages 167--179
\mathnet{http://mi.mathnet.ru/smj7648}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4440272}
\transl
\jour Siberian Math. J.
\yr 2022
\vol 63
\issue 1
\pages 138--148
\crossref{https://doi.org/10.1134/S0037446622010116}
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    • This publication is cited in the following 8 articles:
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