几何凸函数的对称拟算术平均不等式  

The Mean Inequality for Quasi-arithmetic Symmetrical Mean of Geometrically Convex Functions

作　　者：杨镇杭 

机构地区：[1]浙江电力职业技术学院基础部,杭州311600

出　　处：《北京联合大学学报》2005年第3期25-29,共5页Journal of Beijing Union University

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。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.

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 

分 类 号：O174.13[理学—数学]