Remark on Inequalities between Hölder and Lehmer Means
✍ Scribed by Zheng Liu
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 87 KB
- Volume
- 247
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
✦ Synopsis
In 1 Stolarsky established an inequality between the two variable w x means of Holder and Lehmer that is much stronger than that given in 2 .
¨w x However, it should be noted that the inequalities given in 2 are in connection with more general n-variable means. So, it is natural to ask if we could generalize the result of Stolarsky to the n-variable means of Holder and Lehmer with n G 3. Unfortunately, the answer is negative.
📜 SIMILAR VOLUMES
## Abstract We discuss some reversed Hölder inequalities yielding for functions on R~+~ satisfying one or two conditions of quasi‐monotonicity. All cases of equality are pointed out. By using these results and some recent results by the present authors (see [3]), we prove some new reversed inequali
## 1. Definitions and Notations Let (pn) be a sequence of non-negative constants such that po=-O and let A P,, = pk . Then the transformations k-0 n and (1.2) n m=O T n = { P n I -I C Pn-mSm define, respectively, (R, pn) and N ~R L U N D means of the sequence (an), where s , is the partial sum of t