Sharp Bounds for the Weighted Geometric Mean of the First Seiffert and Logarithmic Means in terms of Weighted Generalized Heronian Mean
Optimal bounds for the weighted geometric mean of the first Seiffert and logarithmic means by weighted generalized Heronian mean are proved. We answer the question: for what the greatest value and the least value such that the double inequality, , holds for all with are. Here, and denote the...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/721539 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850230131433406464 |
|---|---|
| author | Ladislav Matejíčka |
| author_facet | Ladislav Matejíčka |
| author_sort | Ladislav Matejíčka |
| collection | DOAJ |
| description | Optimal bounds for the weighted geometric mean of the first Seiffert and logarithmic means by weighted generalized Heronian mean are proved. We answer the question: for what the greatest value and the least value such that the double inequality, , holds for all with are. Here, and denote the first Seiffert, logarithmic, and weighted generalized Heronian means of two positive numbers and respectively. |
| format | Article |
| id | doaj-art-2a0a34fffbce4384bf2d3065546fddaf |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-2a0a34fffbce4384bf2d3065546fddaf2025-08-20T02:03:58ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/721539721539Sharp Bounds for the Weighted Geometric Mean of the First Seiffert and Logarithmic Means in terms of Weighted Generalized Heronian MeanLadislav Matejíčka0Faculty of Industrial Technologies in Púchov, Trenčín University of Alexander Dubček in Trenčín, I. Krasku 491/30, 02001 Púchov, SlovakiaOptimal bounds for the weighted geometric mean of the first Seiffert and logarithmic means by weighted generalized Heronian mean are proved. We answer the question: for what the greatest value and the least value such that the double inequality, , holds for all with are. Here, and denote the first Seiffert, logarithmic, and weighted generalized Heronian means of two positive numbers and respectively.http://dx.doi.org/10.1155/2013/721539 |
| spellingShingle | Ladislav Matejíčka Sharp Bounds for the Weighted Geometric Mean of the First Seiffert and Logarithmic Means in terms of Weighted Generalized Heronian Mean Abstract and Applied Analysis |
| title | Sharp Bounds for the Weighted Geometric Mean of the First Seiffert and Logarithmic Means in terms of Weighted Generalized Heronian Mean |
| title_full | Sharp Bounds for the Weighted Geometric Mean of the First Seiffert and Logarithmic Means in terms of Weighted Generalized Heronian Mean |
| title_fullStr | Sharp Bounds for the Weighted Geometric Mean of the First Seiffert and Logarithmic Means in terms of Weighted Generalized Heronian Mean |
| title_full_unstemmed | Sharp Bounds for the Weighted Geometric Mean of the First Seiffert and Logarithmic Means in terms of Weighted Generalized Heronian Mean |
| title_short | Sharp Bounds for the Weighted Geometric Mean of the First Seiffert and Logarithmic Means in terms of Weighted Generalized Heronian Mean |
| title_sort | sharp bounds for the weighted geometric mean of the first seiffert and logarithmic means in terms of weighted generalized heronian mean |
| url | http://dx.doi.org/10.1155/2013/721539 |
| work_keys_str_mv | AT ladislavmatejicka sharpboundsfortheweightedgeometricmeanofthefirstseiffertandlogarithmicmeansintermsofweightedgeneralizedheronianmean |