On Critical Values of Polynomials with Real Critical Points

被引：0
|
作者：
Aimo Hinkkanen
Ilgiz Kayumov
机构：
[1] University of Illinois at Urbana–Champaign,Department of Mathematics
[2] Kazan State University,Institute of Mathematics and Mechanics
来源：
Constructive Approximation | 2010年 / 32卷
关键词：
Polynomials; Smale’s conjecture; Critical points; Critical values; 30C10; 30C15;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Let f be a polynomial of degree at least 2 with f(0)=0 and f′(0)=1. Suppose that all the zeros of f′ are real. We show that there is a zero ζ of f′ such that |f(ζ)/ζ|≤2/3, and that this inequality can be taken to be strict unless f is of the form f(z)=z+cz3.
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页码：385 / 392
页数：7
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