About Multipoint Distortion Theorems for Rational Functions

Kalmykov S. I

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About Multipoint Distortion Theorems for Rational Functions

机译：关于Rational函数的多点失真定理

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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.

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来源
《Siberian Mathematical Journal》 |2020年第1期|共10页
作者
Kalmykov S. I;
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作者单位

Shanghai Jiao Tong Univ Sch Math Sci Shanghai Peoples R China;

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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
rational functions; Bernstein-type inequalities; multipoint distortion theorems; univalent functions;

机译：理性功能;伯恩斯坦型不等式;多点失真定理;单价函数;

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1. Distortion Theorems and Schlicht Radius for p-Bloch Functions [J] . Xiaohui ZHENG, Jianfei WANG 数学研究及应用：英文版 . 2013,第001期
2. On　Distortion　Theorems　for　the　n－th　Order　Derivative　of　Starlike　and　Convex　Functions　of　Order　α [J] . 凌怡, 盖云英, 包革军哈尔滨工业大学学报：英文版 . 1996,第004期
3. Sharp distortion theorems for rational functions without poles or zeros in simply connected domains [J] . Rudolf Rupp Complex variables and elliptic equations . 2007,第1期

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4. A biparametric family of optimally convergent sixteenth-order multipoint methods with their fourth-step weighting function as a sum of a rational and a generic two-variable function [J] . Geum, Y.H., Kim, Y.I. Journal of Computational and Applied Mathematics . 2011,第10期

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5. Multipoint Schur algorithm and orthogonal rational functions, I: Convergence properties [J] . L. Baratchart, S. Kupin, V. Lunot, Journal d'Analyse Mathématique . 2011,第1期

机译：多点Schur算法和正交有理函数，I：收敛性
6. Explicit Multipoint Rational Interpolation Pade Table for Exponential and Power Functions [C] . A. Zhedanov Workshop on Group Theory and Numerical Analysis . 2005

机译：用于指数和功率函数的显式多点Rational插值Pade表
7. Order of uniform approximation to analytic functions by rational trigonometric and weighted rational functions. [D] . Simmons, Richard D. 1989

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8. Some fixed point theorems for mappings satisfying rational inequality in modular metric spaces with applications [O] . Godwin Amechi Okeke, Daniel Francis, Manuel de la Sen 2020

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9. Distortion Theorems for Rational Functions Without Poles Or Zeros in Simply Connected Domains [O] . Vincent D. Blondel, Rudolf Rupp 2007

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10. An Extension to Rational Functions of a Theorem of J. L. Walsh on Differences of Interpolating Polynomials [R] . Saff, E. B., Sharma, A., Varga, R. S. 1981

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About Multipoint Distortion Theorems for Rational Functions

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