On the derivative of the self-reciprocal polynomials

Let P(z be a polynomial of degree n having no zeros in jzj < k, k 1, and Q(z) = znP(1=z), it is proved by Dewan et al that if jP ′ (z)j and jQ ′ (z)j becomes maximum at the same point on jzj = 1, then max jzj=1 jP ′ (z)j n 1 + kn􀀀 +1 fmax jzj=1 jP(z)j 􀀀 min jzj=k jP(z)jg: In this paper, we Σ obtain a similar result for the polynomials of type P(z) = a0 + n = a z ; 1 n.

کلیدواژه های On the derivative of the self-reciprocal polynomials:

Polynomial ، Inequality ، Maximum modulus ، restricted zeros