A generalization of Alzer's inequality is proved. It is shown that this inequality is satisfied for a large class of increasing convex sequences.
Generalization of H. Alzer's Inequality
β Scribed by Feng Qi
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 47 KB
- Volume
- 240
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
β¦ Synopsis
Using the mathematical induction and Cauchy's mean-value theorem, for any
, where
n and m are natural numbers, k is a nonnegative integer. The lower bound is best w possible. This inequality generalizes the Alzer's inequality J. Math. Anal. Appl. 179 Ε½ .
x 1993 , 396α402 . An open problem is proposed.
π SIMILAR VOLUMES
In this paper we are concerned with the following conjecture. Conjecture: Let L be a collection of k positive integers and In particular, we show this conjecture is true when L consists of k consecutive positive integers. This generalizes a well-known inequality of Fisher's. Our proof simplifies an
Using some results of Maligranda, we obtain a generalization of the well known Jensen's inequality which is also a common generalization of inequalities of Holder Γ€nd Minkowski.
In this paper, we generalize the well-known Holder inequality and give a condition at which the equality holds.