EXTENSION OF AN INEQUALITY OF H. ALZER FOR NEGATIVE POWERS

被引：8
|
作者：
Chen, Chao-Ping [1 ]
Qi, Feng [1 ]
机构：
[1] Jiaozuo Inst Technol, Dept Appl Math & Informat, 142 Mid Jiefang Rd, Jiaozuo City 454000, Henan, Peoples R China
来源：
TAMKANG JOURNAL OF MATHEMATICS | 2005年 / 36卷 / 01期
关键词：
Inequality; power mean; Lagrange's mean value theorem; mathematical indution;
D O I：
10.5556/j.tkjm.36.2005.137
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we show that let n be a natural number, then for all real numbers r, n/n+1 < (1/n Sigma(n)(i=1) i(r) / 1/n + 1 Sigma(n+1)(i=1) i(r) )(1/r) < 1. Both bounds are best possible. This extends a result of H. Alzer, who established this inequality for r > 0
引用
收藏
页码：69 / 72
页数：4
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