Refinement of an Inequality for the Generalized Logarithmic Mean

Chinese Quarterly Journal of Mathematics ›› 2008, Vol. 23 ›› Issue (4): 594-599.

Refinement of an Inequality for the Generalized Logarithmic Mean

1. Department of Electronie Information,Teacher's College ofBeijing Union University,Beijing 100011,China2. Department of Mathematics,Longyan College,Longyan 364012,China

Received:2004-12-20 Online:2008-12-30 Published:2023-09-18
About author:SHI Huan-nan(1948-), male, native of Qidong, Hunan, a professor of Beijing Union University, engages in theory of analytic inequalities.
Supported by:
Supported by the Scientific Research Common Program of Beijing Municipal Commission of Education of China(Km200611417009)； Supported by the Natural Science Foundation of Fujian Province Education Department of China(JA05324)；

Abstract

Abstract: In this article, we show that the generalized logarithmic mean is strictly Schurconvex 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.

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

CLC Number:

O178.1

SHI Huan-nan, WU Shan-he. Refinement of an Inequality for the Generalized Logarithmic Mean[J]. Chinese Quarterly Journal of Mathematics, 2008, 23(4): 594-599.

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Refinement of an Inequality for the Generalized Logarithmic Mean

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