Inequalities for the derivative of rational functions with prescribed poles and restricted zeros

Uzma M. Ahanger, Wal M. Shah
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Abstract

In this paper, instead of assuming that a rational function r(z) with prescribed poles has a zero of order s at origin, we suppose that it has a zero of multiplicity s at any point inside the unit circle, whereas the remaining zeros are within or outside a circle of radius k and prove some results which besides generalizing some inequalities for rational functions include refinements of some polynomial inequalities as special cases.
具有规定极点和限制零点的有理函数导数的不等式
本文不再假设具有规定极点的有理函数r(z)在原点处有一个s阶的零点,而是假设它在单位圆内任意点处有一个s阶的零点,其余零点在半径为k的圆内或圆外,并证明了一些结果,这些结果除了推广有理函数的一些不等式外,还包括一些多项式不等式的特殊改进。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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