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Some Inequalities for the Polynomial with S-Fold Zeros at the Origin

Some Inequalities for the Polynomial with S-Fold Zeros at the Origin
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摘要 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. 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.
作者 Ahmad Zireh Mahmood Bidkham
机构地区 Department of Mathematics Department of Mathematics
出处 《Analysis in Theory and Applications》 CSCD 2016年第1期27-37,共11页 分析理论与应用（英文刊）
关键词 POLYNOMIAL s-fold zeros INEQUALITY maximum modulus derivative. Polynomial, s-fold zeros, inequality, maximum modulus, derivative.
分类号 O174.14 [理学—基础数学] O178 [理学—基础数学]
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参考文献11

  • 1A. Aziz and W. M. Shah, Inequalities for a polynomial and its derivative, Math. Ineq. Appl., 7 (2004), 379-391.
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  • 4K. K. Dewan and S. Hans, Generalization of certain well-known polynomial inequalities, J. Math. Anal. Appl., 363 (2010), 38-41.
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Analysis in Theory and Applications
2016年 第1期

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