On a new generalization of Alzer's inequality

Feng Qi and Lokenath Debnath

International Journal of Mathematics and Mathematical Sciences, 2000, vol. 23, 1-4

Abstract:

Let { a n } 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: a n a n + m ≤ ( ( 1 / n ) ∑ i = 1 n a i r ( 1 / ( n + m ) ) ∑ i = 1 n + m a i r ) 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.

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:698020

DOI: 10.1155/S0161171200003033

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