Let p（z） be a polynomial of degree n, which has no zeros in ｜z｜〈 1, Dewan et al. [K. K. Dewan and Sunil Hans, Generalization of certain well known polynomial inequalities, J. Math. Anal. Appl., 363 （2010）, pp. ...Let p（z） be a polynomial of degree n, which has no zeros in ｜z｜〈 1, Dewan et al. [K. K. Dewan and Sunil Hans, Generalization of certain well known polynomial inequalities, J. Math. Anal. Appl., 363 （2010）, pp. 38-41] established｜zp＇（z）＋nβ/2p（z）｜≤n/2{（｜β/2｜＋｜1＋β/2｜）｜z｜=1max｜p（z）｜-（｜1＋β/2｜-｜β/2｜）｜z｜=1min｜p（z）｜},for any ｜β｜≤ 1 and ｜z｜ = 1. In this paper we improve the above inequality for the polynomial which has no zeros in ｜z｜ 〈 k, k≥ 1, except s-fold zeros at the origin. Our results generalize certain well known polynomial inequalities.展开更多
文摘Let p（z） be a polynomial of degree n, which has no zeros in ｜z｜〈 1, Dewan et al. [K. K. Dewan and Sunil Hans, Generalization of certain well known polynomial inequalities, J. Math. Anal. Appl., 363 （2010）, pp. 38-41] established｜zp＇（z）＋nβ/2p（z）｜≤n/2{（｜β/2｜＋｜1＋β/2｜）｜z｜=1max｜p（z）｜-（｜1＋β/2｜-｜β/2｜）｜z｜=1min｜p（z）｜},for any ｜β｜≤ 1 and ｜z｜ = 1. In this paper we improve the above inequality for the polynomial which has no zeros in ｜z｜ 〈 k, k≥ 1, except s-fold zeros at the origin. Our results generalize certain well known polynomial inequalities.
