Glasnik Matematicki, Vol. 35, No.2 (2000), 215-219.

AN IMPROVED INEQUALITY FOR k-TH DERIVATIVE OF A POLYNOMIAL

V. K. Jain

Mathematics Department, I.I.T., Kharagpur 721302, India

Abstract.   For a polynomial p(z) of degree n, we have obtained a refinement of the well known Bernstein's inequality

max|z|=1 |p(k)(z)| ≤ n(n -1)(n -2)(n -k+1) max|z|=1 |p(z)|.

1991 Mathematics Subject Classification.   30C10, 30A10.

Key words and phrases.   Inequality, zeroes, k-th derivative.

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