Some Results on the Polar Derivative of a Polynomial  

作　　者：Abdullah Mir Bilal Dar 

机构地区：[1]Department of Mathematics, University of Kashmir

出　　处：《Analysis in Theory and Applications》2014年第3期306-317,共12页分析理论与应用（英文刊）

摘　　要：Let P（z） be a polynomial of degree n and for any complex number α, let DαP（z） = nP（z）＋ （α-z）P＇ （z） denote the polar derivative of P（z） with respect to α. In this paper, we obtain certain inequalities for the polar derivative of a polynomial with restricted zeros. Our results generalize and sharpen some well-known polynomial inequalities.Let P（z） be a polynomial of degree n and for any complex number α, let DαP（z） = nP（z）＋ （α-z）P＇ （z） denote the polar derivative of P（z） with respect to α. In this paper, we obtain certain inequalities for the polar derivative of a polynomial with restricted zeros. Our results generalize and sharpen some well-known polynomial inequalities.

关 键 词：POLYNOMIAL ZEROS polar derivative Bemstein inequality. 

分 类 号：O174.14[理学—数学] O636.1[理学—基础数学]