Growth estimates of derivatives of a polynomial

A. Mir

This paper deals with the problem of finding an upper bound for the maximal modulus of the derivative and higher order derivatives of a complex polynomial on a disk under the assumption that the polynomial has no zeros in another disk. The estimates involve the maximal modulus of the polynomial in some disk, the degree, the coefficients and the radii of the disks. 

Tbilisi Mathematical Journal, Vol. 13(2) (2020), pp. 27-37