On Ozeki’s inequality for power sums

Alzer, Horst. "On Ozeki’s inequality for power sums." Czechoslovak Mathematical Journal 50.1 (2000): 99-102. <http://eudml.org/doc/30546>.

@article{Alzer2000,
abstract = {Let $p\in (0,1)$ be a real number and let $n\ge 2$ be an even integer. We determine the largest value $c_n(p)$ such that the inequality \[ \sum ^n\_\{i=1\} |a\_i|^p \ge c\_n(p) \] holds for all real numbers $a_1,\ldots ,a_n$ which are pairwise distinct and satisfy $\min _\{i\ne j\} |a_i-a_j| = 1$. Our theorem completes results of Ozeki, Mitrinović-Kalajdžić, and Russell, who found the optimal value $c_n(p)$ in the case $p>0$ and $n$ odd, and in the case $p\ge 1$ and $n$ even.},
author = {Alzer, Horst},
journal = {Czechoslovak Mathematical Journal},
keywords = {Ozeki inequality},
language = {eng},
number = {1},
pages = {99-102},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On Ozeki’s inequality for power sums},
url = {http://eudml.org/doc/30546},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Alzer, Horst
TI - On Ozeki’s inequality for power sums
JO - Czechoslovak Mathematical Journal
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 1
SP - 99
EP - 102
AB - Let $p\in (0,1)$ be a real number and let $n\ge 2$ be an even integer. We determine the largest value $c_n(p)$ such that the inequality \[ \sum ^n_{i=1} |a_i|^p \ge c_n(p) \] holds for all real numbers $a_1,\ldots ,a_n$ which are pairwise distinct and satisfy $\min _{i\ne j} |a_i-a_j| = 1$. Our theorem completes results of Ozeki, Mitrinović-Kalajdžić, and Russell, who found the optimal value $c_n(p)$ in the case $p>0$ and $n$ odd, and in the case $p\ge 1$ and $n$ even.
LA - eng
KW - Ozeki inequality
UR - http://eudml.org/doc/30546
ER -