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Zbl 1036.26017
Alzer, Horst
On Ozeki's inequality for power sums. (English)
[J] Czech. Math. J. 50, No. 1, 99-102 (2000). ISSN 0011-4642; ISSN 1572-9141/e

Author's summary: ``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 $\sum ^n_{i=1} \vert a_i\vert ^p \ge c_n(p)$ holds for all real numbers $a_1,\ldots ,a_n$ which are pairwise distinct and satisfy $\min _{i\not = j} \break \vert a_i-a_j\vert = 1$. 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.''
[Alois Kufner (Praha)]

MSC 2000:: *26D15 Inequalities for sums, series and integrals of real functions

Keywords: Ozeki inequality

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