| 几何凸函数的对称拟算术平均不等式 |
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| 引用本文： | 杨镇杭.几何凸函数的对称拟算术平均不等式[J].北京联合大学学报(自然科学版),2005,19(3):25-29. |
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| 作者姓名： | 杨镇杭 |
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| 作者单位： | 浙江电力职业技术学院,基础部,杭州,311600 |
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| 摘 要： | 建立了几何凸函数的对称拟算术平均不等式,对文献1]提出的不等式进行了推广统一;引进加权对数幂平均的概念,建立起其与双参数平均之间的关系,得到加权对数平均不等式,从而确定了几何凸函数的几何平均、算术平均的上界的大小关系;最后,提出了几何凸函数的对称拟算术平均不等式的推广问题.
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| 关 键 词： | 几何凸函数 对称拟算术平均 双参数平均 加权对数幂平均 上界 |
| 文章编号： | 1005-0310（2005）03-0025-05 |
| 收稿时间： | 2005-05-16 |
| 修稿时间： | 2005年5月16日 |
The Mean Inequality for Quasi-arithmetic Symmetrical Mean of Geometrically Convex Functions |
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| YANG Zhen-hang.The Mean Inequality for Quasi-arithmetic Symmetrical Mean of Geometrically Convex Functions[J].Journal of Beijing Union University,2005,19(3):25-29. |
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| Authors: | YANG Zhen-hang |
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| Abstract: | An inequality for quasi-arithmetic symmetrical mean of geometrically convex functions is established, and inequalities presented by article 1 ] are unified and generalized. The concept of the weighted logarithmic power mean is introduced; its relation with two-parameter mean is given; the inequality for weighted logarithmic power mean is derived; the magnitude relation among upper bounds of geometric mean and arithmetic mean of geometrically convex functions are made certain. A problem of generalization on inequality for quasi-arithmetic symmetrical mean of geometrically convex functions is put forward. |
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| Keywords: | geometrically convex functions quasi-arithmetic symmetrical mean two-parameter mean weighted logarithmic power mean upper bound |
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