SOME INEQUALITIES
FOR THE DERIVATIVE OF A POLYNOMIAL
Nisar Ahmad Rather1, Sajad Hussian Ahangar2, Mushtaq Ahmad Shah3
1,2,3P.G. Department of Mathematics
University of Kashmir
Srinagar, Hazratbal, 190006, INDIA
Abstract. Let Pn(z) denote the space of all complex polynomials P(z)=∑j=0najzj of degree n. According to a well known inequality of S. Bernstein, if P ∈ Pn, then |z|=Max |P'(z)| ≤ n |z|=Max |P(z)|.

In this paper, we establish some generalizations and refinements of the above inequality and some other well known inequalities concerning the polynomials and their derivatives.

AMS Subject Classification: 30A06, 30A64, 30C10
Key Words and Phrases: polynomials, inequalities, complex domain


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DOI: 10.12732/ijam.v26i2.4

Volume: 26
Issue: 2
Year: 2013