Various versions of Bernstein and Turán-type inequalities are a classical topic in analysis. Over a period, these inequalities have been generalized for different classes of functions. Here, we establish some new comparison inequalities for rational functions in the complex plane that are inspired by some classical inequalities of Bernstein and Turán type. The obtained results produce extensions of many inequalities for polynomials as special cases.

中文翻译：

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具有指定极点的有理函数之间的比较不等式

Bernstein和Turán型不等式的各种版本是分析中的经典话题。一段时间以来，这些不等式已针对不同类别的函数进行了推广。在这里，我们受伯恩斯坦和图兰类型的一些经典不等式的启发，为复平面中的有理函数建立了一些新的比较不等式。获得的结果将多项式的许多不等式作为特殊情况进行了扩展。