An inequality of W. L. Wang and P. F. Wang
In this note we present a proof of the inequality Hn/H′n≤Gn/G′n where Hn and Gn (resp. H′n and G′n) denote the weighted harmonic and geometric means of x1,…,xn (resp. 1−x1,…,1−xn) with xi∈(0,1/2], i=1,…,n.
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
1990-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171290000436 |
| id |
doaj-6af98ca6bef548f4a9f0c56cfaf25632 |
|---|---|
| record_format |
Article |
| spelling |
doaj-6af98ca6bef548f4a9f0c56cfaf256322020-11-25T00:32:59ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251990-01-0113229529810.1155/S0161171290000436An inequality of W. L. Wang and P. F. WangHorst Alzer0Department of Mathematics, University of the Witwatersrand, Johannesburg, South AfricaIn this note we present a proof of the inequality Hn/H′n≤Gn/G′n where Hn and Gn (resp. H′n and G′n) denote the weighted harmonic and geometric means of x1,…,xn (resp. 1−x1,…,1−xn) with xi∈(0,1/2], i=1,…,n.http://dx.doi.org/10.1155/S0161171290000436geometric and harmonic meansinequalities. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Horst Alzer |
| spellingShingle |
Horst Alzer An inequality of W. L. Wang and P. F. Wang International Journal of Mathematics and Mathematical Sciences geometric and harmonic means inequalities. |
| author_facet |
Horst Alzer |
| author_sort |
Horst Alzer |
| title |
An inequality of W. L. Wang and P. F. Wang |
| title_short |
An inequality of W. L. Wang and P. F. Wang |
| title_full |
An inequality of W. L. Wang and P. F. Wang |
| title_fullStr |
An inequality of W. L. Wang and P. F. Wang |
| title_full_unstemmed |
An inequality of W. L. Wang and P. F. Wang |
| title_sort |
inequality of w. l. wang and p. f. wang |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
1990-01-01 |
| description |
In this note we present a proof of the inequality Hn/H′n≤Gn/G′n where Hn and Gn (resp. H′n and G′n) denote the weighted harmonic and geometric means of x1,…,xn (resp. 1−x1,…,1−xn) with xi∈(0,1/2], i=1,…,n. |
| topic |
geometric and harmonic means inequalities. |
| url |
http://dx.doi.org/10.1155/S0161171290000436 |
| work_keys_str_mv |
AT horstalzer aninequalityofwlwangandpfwang AT horstalzer inequalityofwlwangandpfwang |
| _version_ |
1725317910359965696 |