#### 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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