Rado不等式的多参数推广及应用

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.

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

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 well-known 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.