Inequalities concerning polar derivative of polynomials

Arty Ahuja, K. K. Dewan, Sunil Hans


In this paper we obtain certain results for the polar derivative of a polynomial \(p(z) = c_nz^n +\sum_{j=\mu}^n c_{n-j}z^{n-j}\), \(1\leq\mu\leq n\), having all its zeros on \(|z| = k\), \(k\leq 1\), which generalizes the results due to Dewan and Mir, Dewan and Hans. We also obtain certain new inequalities concerning the maximum modulus of a polynomial with restricted zeros.
[Editor's note: There are flaws in the paper, see M. A. Qazi, Remarks on some recent results about polynomials with restricted zeros, Ann. Univ. Mariae Curie-Skłodowska Sect. A 67 (2), (2013), 59-64 ]


Polynomials; maximum modulus; inequalities in the complex domain; polar derivative

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Data publikacji: 2016-07-25 18:17:30
Data złożenia artykułu: 2016-07-25 14:20:08


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