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.