(untitled) (Analysis in Theory and Applications, 2013)
Let P(z) be a polynomial of degree n having no zeros in |z|< 1, then for every real or complex number β with |β|≤ 1, and |z|=1, R≥ 1, it is proved by Dewan et al. [4] that|P(Rz)+β(R+12)^n P(z)|≤12{(|R^n+β(R+12)^n|+|1+β(R+12)^n|)_|z|=1|P(z)| -(|R^n+β(R+12)^n|-|1+β(R+12)^n|)_|z|=1|P(z)|}. In this paper we generalize the above inequality for polynomials having no zeros in |z| < k, k≤ 1. Our results generalize certain well-known polynomial inequalities.