Displaying similar documents to “On growth of polynomials.”

On maximum modulus for the derivative of a polynomial

K. Dewan, Sunil Hans (2009)

Annales UMCS, Mathematica

Similarity:

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.

Inequalities concerning polar derivative of polynomials

Arty Ahuja, K. Dewan, Sunil Hans (2011)

Annales UMCS, Mathematica

Similarity:

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.

Growth of polynomials whose zeros are outside a circle

K. Dewan, Sunil Hans (2008)

Annales UMCS, Mathematica

Similarity:

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.

Single polynomials that correspond to pairs of cyclotomic polynomials with interlacing zeros

James McKee, Chris Smyth (2013)

Open Mathematics

Similarity:

We give a complete classification of all pairs of cyclotomic polynomials whose zeros interlace on the unit circle, making explicit a result essentially contained in work of Beukers and Heckman. We show that each such pair corresponds to a single polynomial from a certain special class of integer polynomials, the 2-reciprocal discbionic polynomials. We also show that each such pair also corresponds (in four different ways) to a single Pisot polynomial from a certain restricted class,...