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.