This article is cited in 11 papers

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

G. V. Milovanovich^ab, A. Mir^c, A. Hussain<sup>c

a</sup> 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.

UDC: 517.538

Received: 05.02.2021
Revised: 06.06.2021
Accepted: 11.10.2021

DOI: 10.33048/smzh.2022.63.111

 English version: Siberian Mathematical Journal, 2022, 63:1, 138–148

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