# Article

 Title: On Ozeki’s inequality for power sums (English) Author: Alzer, Horst Language: English Journal: Czechoslovak Mathematical Journal ISSN: 0011-4642 (print) ISSN: 1572-9141 (online) Volume: 50 Issue: 1 Year: 2000 Pages: 99-102 Summary lang: English . Category: math . 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 $\sum ^n_{i=1} |a_i|^p \ge c_n(p)$ 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. (English) MSC: 26D15 idZBL: Zbl 1036.26017 idMR: MR1745464 . Date available: 2009-09-24T10:30:36Z Last updated: 2016-04-07 Stable URL: http://hdl.handle.net/10338.dmlcz/127553 . Reference: [1] D.S. Mitrinović and G. Kalajdžić: On an inequality.Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. 678–715 (1980), 3–9. MR 0623215 Reference: [2] N. Ozeki: On the estimation of inequalities by maximum and minimum values.J. College Arts Sci. Chiba Univ. 5 (1968), 199–203. (Japanese) MR 0254198 Reference: [3] D.C. Russell: Remark on an inequality of N. Ozeki.General Inequalities 4, W. Walter (ed.), Birkhäuser, Basel, 1984, pp. 83–86. MR 0821787 .

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