Rado不等式的多参数推广及应用  

Generalization of Rado′s Inequality Involving Multiple Parameters and Its Applications

作　　者：邓勇平[1] 吴善和[1] 

机构地区：[1]龙岩学院数学系,福建龙岩364012

出　　处：《数学的实践与认识》2006年第10期205-209,共5页Mathematics in Practice and Theory

基　　金：福建省教育厅科技项目(JA05324)

摘　　要：通过引入加权幂平均以及参数α、β、μ建立一个新的R ado型不等式,由于所得不等式中含多个参数,因此是一个非常广泛的结果,可以通过对参数的适当取值得到一些已知结果的改进(如著名的Popov iciu不等式的改进),同时也可获得许多新的不等式.最后,我们应用所得结果给出加权幂平均不等式以及加权平均不等式的加细形式.A new Rado-type inequality is established by introducing weighted power means and parameters α,β,μ. The obtained inequality involving multiple parameters is a very geenral result. By assigning appropriate values to the parameters, some known results such as the wellknown Popoviciu＇s inequality can be imrpoved, also a number of new inequalities can be deduced. Finally, we provide an application of obtained result to the refinement of weighted power means inequality and weighted means inequality.

关 键 词：Rado不等式 Popoviciu不等式 加权平均 幂平均 参数 推广 

分 类 号：O178[理学—数学]