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ЖУРНАЛЫ // Проблемы анализа — Issues of Analysis // Архив

Пробл. анал. Issues Anal., 2024, том 13(31), выпуск 1, страницы 3–23 (Mi pa388)

Smirnov and Bernstein-type inequalities, taking into account higher-order coefficients and free terms of polynomials

E. G. Kompaneets, L. G. Zybina

Petrozavodsk State University, 33 Lenina pr., Petrozavodsk 185910, Russia

Аннотация: The starting point in the theory of differential inequalities for polynomials is the book "Investigation of aqueous solutions by specific gravity" by D. I. Mendeleev. In this work, he dealt not only with chemical, but also mathematical problems. The question raised in this book led to appearance of a large number of works on various types of differential inequalities for polynomials. In our paper, we obtain Smirnov and Bernstein-type inequalities that use higher-order coefficients and free terms of polynomials.

Ключевые слова: polynomial, differential inequality, higher-order coefficient, free term.

УДК: 517.83

MSC: 30C10, 30A10

Поступила в редакцию: 15.07.2023
Принята в печать: 03.11.2023

Язык публикации: английский

DOI: 10.15393/j3.art.2024.14270



© МИАН, 2024