一类新的Shapiro型不等式及其应用

A class of new Shapiro type inequalities and their applications

给出一类新的Shapiro型不等式,在代数不等式研究中有着广泛的应用,利用它们可直接得到一大批新的分式型不等式,也可运用它们证明或推广许多不等式,推广和发展了一些近期的结果。

In this paper, we establish a class of new Shapiro type inequalities,which has found wide application in algebraic inequality. With a powerful tool, we can not only improve a number of fractional inequalities and discover some new ones, but can prove or generalize a lot of inequalities to promote and develop some author＇s recent results.