论文标题
某些类别的理性功能的衍生物的界限
Bounds of the Derivative of Some Classes of Rational Functions
论文作者
论文摘要
令$ r（z）$成为有理功能，最多使用$ n $ poles，$ a_1，a_2，\ ldots，a_n，$ | a_j | > 1，$ 1 \ $ 1 \ leq j \ leqn。$本文研究了单位圈子上有理函数$ r（z）$的模量的估计。当$ r（z）$的所有零位于$ | z | \ geq k \ geq 1 $中时，我们就建立了一个上限伯恩斯坦类型的理性功能不平等，格拉斯。 Mat。，{\ bf 32}（52）（1997），29--37。]。
Let $r(z)$ be a rational function with at most $n$ poles, $a_1, a_2, \ldots, a_n,$ where $|a_j| > 1,$ $1\leq j\leq n.$ This paper investigates the estimate of the modulus of the derivative of a rational function $r(z)$ on the unit circle. We establish an upper bound when all zeros of $r(z)$ lie in $|z|\geq k\geq 1$ and a lower bound when all zeros of $r(z)$ lie in $|z|\leq k \leq 1.$ In particular, when $k=1$ and $r(z)$ has exactly $n$ zeros, we obtain a generalization of results by A. Aziz and W. M. Shah [Some refinements of Bernstein-type inequalities for rational functions, Glas. Mat., {\bf 32}(52) (1997), 29--37.].
