(untitled) (Analysis in Theory and Applications, 2018)
Let P(z) be a polynomial of degree n having all its zeros in |z|≤k, k≤1, then for every real or complex number β, with |β|≤1 and R≥1, it was shown by A. Zireh et al. [7] that for |z|=1, _|z|=1|P(Rz)+β(R+k1+k)^nP(z)|≥ k^-n|R^n+β(R+k1+k)^n|_|z|=k|P(z)|. In this paper, we shall present a refinement of the above inequality. Besides, we shall also generalize some well-known results.