on a new generalization of alzer's inequality
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ID: 182865
2000
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Abstract
Let {an}n=1∞ be an increasing sequence of positive
real numbers. Under certain conditions of this sequence we use the
mathematical induction and the Cauchy mean-value theorem to prove
the following inequality:
anan+m≤((1/n)∑i=1nair(1/(n+m))∑i=1n+mair)1/r, where n and m are natural numbers and r is a positive number.
The lower bound is best possible. This inequality generalizes the
Alzer's inequality (1993) in a new direction. It is shown that the
above inequality holds for a large class of positive, increasing
and logarithmically concave sequences.
| Reference Key |
qi2000internationalon
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|---|---|
| Authors | ;Feng Qi;Lokenath Debnath |
| Journal | structural engineering and mechanics |
| Year | 2000 |
| DOI |
10.1155/S0161171200003033
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| URL | |
| Keywords |
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