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This article is cited in 4 scientific papers (total in 4 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
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.
Received: 05.02.2021 Revised: 06.06.2021 Accepted: 11.10.2021
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
Linking options:
https://www.mathnet.ru/eng/smj7648 https://www.mathnet.ru/eng/smj/v63/i1/p167
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Abstract page: | 96 | Full-text PDF : | 36 | References: | 15 | First page: | 17 |
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