Vol. 11, No 2: 85–96.

Mathematics and Mechanics

 2026

Scientific article

UDK 517.53
pdf-version

Ivan A. Samsonov
bachelor’s degree, Petrozavodsk State University
(Petrozavodsk, Russia),
vanya05samson73@mail.ru

Smirnov-Type Inequality for Polynomials with One Zero in the Left Half-Plane

Scientific adviser:
Ekaterina G. Kompaneets
Reviewer:
Victor Starkov
Paper submitted on: 05/13/2026;
Accepted on: 06/27/2026;
Published online on: 06/27/2026.
 Abstract. In 1887, D. I. Mendeleev posed the following mathematical problem: for a polynomial f,|f(x)|≤M, x∈[a,b], estimate |f'(x)|. This question has generated a large number of papers on various types of differential inequalities for polynomials. In classical studies, it was assumed that all the zeros of the majorizing polynomial lie in the same region (for example, in the unit circle, the right half-plane, etc.). We remove this requirement by assuming that one zero lies in the left half-plane and the others lie in the right half-plane. This paper obtains an analogue of the Smirnov inequality for such polynomials.
Keywords: polynomials, Smirnov-type inequality, Smirnov operator

For citation: Samsonov, I. A. Smirnov-Type Inequality for Polynomials with One Zero in the Left Half-Plane. StudArctic forum. 2026, 11 (2): 85–96.

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