| 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:
|
2020-07-03 |
| 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 |
| . |
