Inequalities for a polynomial and its derivative

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:336

Article

Chanam, Barchand ; Dewan, K. K.

关键词: polynomials;    maximum modulus;    inequalities;    derivative;    Rivlin's theorem;   

DOI  :  10.1016/j.jmaa.2007.02.029

来源: Elsevier

【 摘 要 】

[GRAPHICS] Equality holds for the polynomial p(z) = (z(mu) + k(mu))(n/mu) where n is a multiple of mu. In this paper, we obtain an improvement of the above inequality by involving some of the coefficients. As an application of our result, we further improve upon a result recently proved by Aziz and Shah [A. Aziz, W.M. Shah, Inequalities for a polynomial and its derivative, Math. Inequal. Appl. 7 (3) (2004) 379-391]. (c) 2007 Elsevier Inc. All rights reserved.

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