In this paper we establish a family of comparison inequalities between rational functions with prescribed poles for the sup-norms on the unit circle in the complex plane. Certain estimates for the modulus of the derivative of rational functions as well as some inequalities of Turán’s type are also obtained. The obtained results produce many inequalities for polynomials and polar derivatives as special cases.

中文翻译：

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亚单位函数在单位圆盘边界上的导数的某些估计

在本文中，我们为复平面上单位圆上的超范数建立了带有指定极点的有理函数之间的比较不等式族。还获得了对有理函数导数模量的某些估计，以及一些图兰类型的不等式。作为特殊情况，所得结果对于多项式和极导数产生了许多不等式。