Geodesic
A Unitary Treatment of Certain Inequalities Involving Means
Kragujevac Journal of Mathematics, Tome 45 (2021) no. 2, p. 181 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

The aim of this paper is to state and prove certain inequalities that involve means (e.g., the arithmetic, geometric, logarithmic means) using a particular result. First of all we recall useful properties of a real-valued convex function that will be used in the proof of our inequalities. Further, we present three inequalities, the first involving the logarithmic mean, the second involving the classical arithmetical and geometrical means and in the last we introduce a new mean. Finally, we give alternate proofs to the Schweitzer's inequality and Khanin's inequality.
Classification : 26D20 26A51, 26B25
Keywords: generalized mean, logarithmic mean, convex function, maximum point 
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A. F. Albişoru; M. Stroe. A Unitary Treatment of Certain Inequalities Involving Means. Kragujevac Journal of Mathematics, Tome 45 (2021) no. 2, p. 181 . http://geodesic.mathdoc.fr/item/KJM_2021_45_2_a1/