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 t...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.展开更多
The paper brings an important integral inequality, which includes the famous Polya-Szego inequality and the logarithmical-arithmetic mean inequality as special cases.
基金Foundation item： Supported by the Scientific Research Common Program of Beijing Municipal Commission of Education of China（Km200611417009） Suppoted by the Natural Science Foundation of Fujian Province Education Department of China（JA05324）
文摘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.
基金the Scientific Research fund of Pingyuan University(2005006)
文摘The paper brings an important integral inequality, which includes the famous Polya-Szego inequality and the logarithmical-arithmetic mean inequality as special cases.
