Let P（z） be a polynomial of degree n having no zeros in ｜z｜〈 1, then for every real or complex number β with ｜β｜≤ 1, and ｜z｜ = 1, R ≥ 1, it is proved by Dewan et al. [4] that｜P（Rz）＋β（R＋1/2）^nP（z...Let P（z） be a polynomial of degree n having no zeros in ｜z｜〈 1, then for every real or complex number β with ｜β｜≤ 1, and ｜z｜ = 1, R ≥ 1, it is proved by Dewan et al. [4] that｜P（Rz）＋β（R＋1/2）^nP（z）｜≤1/2{（｜R^n＋β（R＋1/2）^n｜＋｜1＋β（R＋1/2）^n｜max｜z｜=1｜P（z）｜ -（｜R^n＋β（R＋1/2）^n｜-｜1＋β（R＋1/2）^n｜max｜z｜=1｜P（z）｜}.In this paper we generalize the above inequality for polynomials having no zeros in }z} 〈 k, k ≤ 1. Our results generalize certain well-known polynomial inequalities.展开更多
文摘Let P（z） be a polynomial of degree n having no zeros in ｜z｜〈 1, then for every real or complex number β with ｜β｜≤ 1, and ｜z｜ = 1, R ≥ 1, it is proved by Dewan et al. [4] that｜P（Rz）＋β（R＋1/2）^nP（z）｜≤1/2{（｜R^n＋β（R＋1/2）^n｜＋｜1＋β（R＋1/2）^n｜max｜z｜=1｜P（z）｜ -（｜R^n＋β（R＋1/2）^n｜-｜1＋β（R＋1/2）^n｜max｜z｜=1｜P（z）｜}.In this paper we generalize the above inequality for polynomials having no zeros in }z} 〈 k, k ≤ 1. Our results generalize certain well-known polynomial inequalities.
