Some compact generalization of inequalities for polynomials with prescribed zeros

‎Let p(z)=zsh(z) where h(z) is a polynomial‎ ‎of degree at most n−s having all its zeros in |z|≥k or in |z|≤k‎. ‎In this paper we obtain some new results about the dependence of |p(Rz)| on |p(rz)| for r²≤rR≤k²‎, ‎k²≤rR≤R² and for R≤r≤k‎. ‎Our results refine and generalize certain well-known polynomial inequalities‎.