On the proof of Erdős' inequality

Title:

On the proof of Erdős' inequality

Creator:

Zhu, Lai-Yi and Zhou, Da-Peng

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:2c3ea0a2-0da8-4457-acfa-a4e78aba913d
uuid:2c3ea0a2-0da8-4457-acfa-a4e78aba913d
issn:0011-4642

Subject:

polynomy, mathematics, polynomials, Erdős' inequality, undergraduate calculus, monotone polynomial, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

Using undergraduate calculus, we give a direct elementary proof of a sharp Markov-type inequality $\|p'\|_{[-1,1]}\leq\frac12\|p\|_{[-1,1]}$ for a constrained polynomial $p$ of degree at most $n$, initially claimed by P. Erdős, which is different from the one in the paper of T. Erdélyi (2015). Whereafter, we give the situations on which the equality holds. On the basis of this inequality, we study the monotone polynomial which has only real zeros all but one outside of the interval $(-1,1)$ and establish a new asymptotically sharp inequality., Lai-Yi Zhu, Da-Peng Zhou., and Obsahuje bibliografii

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

967-979

Source:

Czechoslovak Mathematical Journal | 2017 Volume:67 | Number:4

Harvested from:

CDK

Metadata only:

false