About Multipoint Distortion Theorems for Rational Functions

Сибирский математический журнал

article

S. I. Kalmykov¹ 

[1] School of Mathematical Sciences, Shanghai Jiao Tong University;Institute of Applied Mathematics

关键词: rational functions;    Bernstein-type inequalities;    multipoint distortion theorems;    univalent functions;   

DOI  :  10.1134/S0037446620010073

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

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.

【 授权许可】

CC BY