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,min|z|=1|P(Rz)+β((R+k)...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,min|z|=1|P(Rz)+β((R+k)/(1+k))~nP(z)|≥k^(-n)|R^n+β((R+k)/(1+k))~n|min|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.展开更多
文摘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,min|z|=1|P(Rz)+β((R+k)/(1+k))~nP(z)|≥k^(-n)|R^n+β((R+k)/(1+k))~n|min|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.
