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On maximum modulus for the derivative of a polynomial

K. DewanSunil Hans — 2009

Annales UMCS, Mathematica

If P(z) is a polynomial of degree n, having all its zeros in the disk [...] then it was shown by Govil [Proc. Amer. Math. Soc. 41, no. 2 (1973), 543-546] that [...] In this paper, we obtain generalization as well as improvement of above inequality for the polynomial of the type [...] Also we generalize a result due to Dewan and Mir [Southeast Asian Bull. Math. 31 (2007), 691-695] in this direction.

Growth of polynomials whose zeros are outside a circle

K. DewanSunil Hans — 2008

Annales UMCS, Mathematica

If p(z) be a polynomial of degree n, which does not vanish in |z| < k, k < 1, then it was conjectured by Aziz [Bull. Austral. Math. Soc. 35 (1987), 245-256] that [...] In this paper, we consider the case k < r < 1 and present a generalization as well as improvement of the above inequality.

Inequalities concerning polar derivative of polynomials

Arty AhujaK. DewanSunil Hans — 2011

Annales UMCS, Mathematica

In this paper we obtain certain results for the polar derivative of a polynomial [...] , having all its zeros on [...] 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.

Inequalities concerning polar derivative of polynomials

Arty AhujaK. K. DewanSunil Hans — 2011

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

In this paper we obtain certain results for the polar derivative of a polynomial p ( z ) = c n z n + j = μ n c n - j z n - j , 1 μ n , having all its zeros on | z | = k , k 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 ]

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