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Bounds for the Differences between Arithmetic and Geometric Means and Their Applications to Inequalities
- Source :
- Symmetry, Vol 13, Iss 2398, p 2398 (2021), Symmetry; Volume 13; Issue 12; Pages: 2398
- Publication Year :
- 2021
- Publisher :
- MDPI AG, 2021.
-
Abstract
- Refining and reversing weighted arithmetic-geometric mean inequalities have been studied in many papers. In this paper, we provide some bounds for the differences between the weighted arithmetic and geometric means, using known inequalities. We improve the results given by Furuichi-Ghaemi-Gharakhanlu and Sababheh-Choi. We also give some bounds on entropies, applying the results in a different approach. We explore certain convex or concave functions, which are symmetric functions on the axis t=1/2.
- Subjects :
- Physics and Astronomy (miscellaneous)
General Mathematics
Shannon entropy
Computer Science::Digital Libraries
Bose–Einstein entropy
arithmetic mean
Fermi–Dirac entropy
geometric mean
Chemistry (miscellaneous)
Computer Science (miscellaneous)
Tsallis entropy
Young’s inequality
QA1-939
Computer Science::Programming Languages
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 20738994
- Volume :
- 13
- Issue :
- 2398
- Database :
- OpenAIRE
- Journal :
- Symmetry
- Accession number :
- edsair.doi.dedup.....cc093c1839c10abaeb8c0e2ad19aa800