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Extension of the refined Gibbs' inequality
Problemy analiza, Tome 6 (2017) no. 1, pp. 3-10 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this note, we give an extension of the refined Gibbs' inequality containing arithmetic and geometric means. As an application, we obtain converse and refinement of the arithmetic-geometric mean inequality.
Keywords: arithmetic-geometric mean inequality, Jensen's inequality, log-function, Gibbs' inequality. 
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V. Adiyasuren; Ts. Batbold. Extension of the refined Gibbs' inequality. Problemy analiza, Tome 6 (2017) no. 1, pp. 3-10. http://geodesic.mathdoc.fr/item/PA_2017_6_1_a0/

[1] Adiyasuren V., Batbold Ts., Adil Khan M., “Refined arithmetic-geometric mean inequality and new entropy upper bound”, Commun. Korean Math. Soc., 31:1 (2016), 95–100 | DOI | MR | Zbl

[2] Alzer H., “On an inequality from information theory”, Rend. Istit. Mat. Univ. Trieste, 46 (2012), 231–235 | MR

[3] Beckenbach E. F., Bellman R., Inequalities, Springer Verlag, Berlin, 1983 | MR | Zbl

[4] Bullen P. S., Mitrinović D. S., Vasić P. M., Means and their inequalities, Reidel, Dordrecht, 1988 | MR | Zbl

[5] Gao P., “A new approach to Ky Fan-type inequalities”, Int. J. Math. Math. Sci., 2005, no. 22, 3551–3574 | DOI | MR | Zbl

[6] Halliwell G. T., Mercer P. R., “A refinement of an inequality from information theory”, J. Inequal. Pure Appl. Math., 5:1 (2004), 1–3 | MR | Zbl

[7] Hardy G. H., Littlewood J. E., Pólya G., Inequalities, Cambridge University Press, Cambridge, 1954 | MR

[8] Mitrinović D. S., Analytic inequalities, Springer Verlag, New York, 1970 | MR | Zbl

[9] Parkash O., Kakkar P., “Entropy bounds using arithmetic-geometricharmonic mean inequality”, Int. J. Pure Appl. Math., 89:5 (2013), 719–730 | DOI

[10] Simic S., “Jensen's inequality and new entropy bounds”, Appl. Math. Lett., 22 (2009), 1262–1265 | DOI | MR | Zbl

[11] Tian J., “New property of a generalized Hölder's inequality and its applications”, Information Sciences, 288 (2014), 45–54 | DOI | MR | Zbl