On the proof of Erdős' inequality
Czechoslovak Mathematical Journal (2017)
- Volume: 67, Issue: 4, page 967-979
- ISSN: 0011-4642
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topZhu, Lai-Yi, and Zhou, Da-Peng. "On the proof of Erdős' inequality." Czechoslovak Mathematical Journal 67.4 (2017): 967-979. <http://eudml.org/doc/294757>.
@article{Zhu2017,
abstract = {Using undergraduate calculus, we give a direct elementary proof of a sharp Markov-type inequality $\Vert p^\{\prime \}\Vert _\{[-1,1]\}\le \frac\{1\}\{2\}\Vert p\Vert _\{[-1,1]\}$ 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.},
author = {Zhu, Lai-Yi, Zhou, Da-Peng},
journal = {Czechoslovak Mathematical Journal},
keywords = {polynomial; Erdős’ inequality; undergraduate calculus; monotone polynomial},
language = {eng},
number = {4},
pages = {967-979},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the proof of Erdős' inequality},
url = {http://eudml.org/doc/294757},
volume = {67},
year = {2017},
}
TY - JOUR
AU - Zhu, Lai-Yi
AU - Zhou, Da-Peng
TI - On the proof of Erdős' inequality
JO - Czechoslovak Mathematical Journal
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 4
SP - 967
EP - 979
AB - Using undergraduate calculus, we give a direct elementary proof of a sharp Markov-type inequality $\Vert p^{\prime }\Vert _{[-1,1]}\le \frac{1}{2}\Vert p\Vert _{[-1,1]}$ 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.
LA - eng
KW - polynomial; Erdős’ inequality; undergraduate calculus; monotone polynomial
UR - http://eudml.org/doc/294757
ER -
References
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