On the derivative of the self-reciprocal polynomials

Let P(z be a polynomial of degree n having no zeros in jzj < k, k ۱, and Q(z) = znP(۱=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 = ۱, then max jzj=۱ jP ′ (z)j n ۱ + kn􀀀 +۱ fmax jzj=۱ 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) = a۰ + n = a z ; ۱ n.

کلیدواژه ها:

Polynomial ، Inequality ، Maximum modulus ، restricted zeros