This article is cited in 10 papers

About multipoint distortion theorems for rational functions

S. I. Kalmykov<sup>ab

a</sup> School of Mathematical Sciences, Shanghai Jiao Tong University
^b Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok

Abstract: We prove some two- and three-point distortion theorems for rational functions that generalize some recent results on Bernstein-type inequalities for polynomials and rational functions. The rational functions under study have either majorants or restrictions on location of their zeros. The proofs are based on the new version of the Schwarz Lemma and univalence condition for regular functions which was suggested by Dubinin.

Keywords: rational functions, Bernstein-type inequalities, multipoint distortion theorems, univalent functions.

UDC: 517.54

MSC: 35R30

Received: 15.02.2019
Revised: 25.03.2019
Accepted: 15.05.2019

DOI: 10.33048/smzh.2020.61.107

 English version: Siberian Mathematical Journal, 2020, 61:1, 85–94

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