We prove some two- and three-point distortion theorems for rational functions that generalize some recent results on Bernstein-type inequalities for polynomials and rational functions. The rational functions under study have either majorants or restrictions on location of their zeros. The proofs are based on the new version of the Schwarz Lemma and univalence condition for regular functions which was suggested by Dubinin.

中文翻译：

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关于有理函数的多点失真定理

我们证明了有理函数的一些两点和三点失真定理，这些定理概括了多项式和有理函数的伯恩斯坦型不等式的一些最新结果。所研究的有理函数对其零点的位置要么有主项要么有限制。证明基于新版本的 Schwarz Lemma 和 Dubinin 建议的正则函数的单价条件。