An algebraic inequality (Q2710148)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An algebraic inequality |
scientific article |
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13 May 2001
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Cauchy mean-value theorem
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Alzer inequality
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algebraic inequalities
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An algebraic inequality (English)
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The following inequality is proved: NEWLINE\[NEWLINE[((b+ k-a)/(b- a))\cdot (b^{r+ 1}- a^{r+1})/((b+ k)^{r+ 1}- a^{r+1})]^{1/r}> b/(b+ k)NEWLINE\]NEWLINE for all \(b> a> 0\) and \(k> 0\) real numbers. This can be written also as an integral analogue of a generalized Alzer inequality.NEWLINENEWLINENEWLINE\{Reviewer's remark: The author has written more papers by using a nice argument (based on induction and Cauchy's theorem), without mentioning (as here) that the first paper is due to the reviewer [J. Math. Anal. Appl. 192, No. 3, 1034-1035 (1995; Zbl 0829.26013)]\}.
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