Chin, Quart . J. of Math．2008, 23 (4): 594— 599.

Refinement of an Inequality for the Generalized Logarithmic Mean 

Shi Huan-nan, Wu Shan-he

Abstract: In this article, we show that the generalized logarithmic mean is strictly Schur-convex function for p > 2 and strictly Schur-concave function for p < 2 on R^2_+. And then we give a refinement of an inequality for the generalized logarithmic mean inequality using a simple majoricotion relation of the vector.

Keywords: inequality, refinement, generalized logarithmic mean, strictly Schur-convex function, strictly Schur-concave function

MR(2000) Subject Classification: 26D15

Chinese Library Classification: O178.1

Refinement_of_an_Inequality_for_the_Generalized_Logarithmic_Mean.pdf