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On the maximum modulus of a polynomial

Jain Vinay Kumar

Journal of Mathematics and Applications

2019

Vol. 42

109--116

For a polynomial p(z) of degree n, having no zeros in |z| < 1 Ankeny and Rivlin had shown that for R ≥ 1 [wzór]. Using Govil, Rahman and Schmeisser’s refinement of the generalization of Schwarz’s lemma we have obtained a refinement of Ankeny and Rivlin’s result. Our refinement is also a refinement of Dewan and Pukhta’s refinement of Ankeny and Rivlin’s result.

Growth estimates of composite entire functions in the light of slowly changing functions based relative order, relative type and relative weak type

Datta S. K., Biswas T., Bhattacharyya S.

Fasciculi Mathematici

2015

Nr 54

59--74

In the paper we prove some growth properties of maximum term and maximum modulus of composition of entire functions on the basis of relative L*-order, relative L*-type and relative L*-weak type.

Some inequalities for the polar derivative of a polynomial with restricted zeros

Zireh A., Hosseini S. A.

Journal of Mathematics and Applications

2014

Vol. 37

119--129

Let p(z) be a polynomial of degree n and for any complex number (alfa), D(alfa)p(z) = np(z)+(alfa-z)p′(z) denote the polar derivative of the polynomial p(z) with respect to. In this paper, we obtain new results concerning maximum modulus of the polar derivative of a polynomial with restricted zeros. Our result generalize certain well-known polynomial inequalities.