(untitled) (Analysis in Theory and Applications, 2017)
Let p(z)=a_0+a_1z+a_2z^2+a_3z^3+…+a_nz^n be a polynomial of degree n. Rivlin [12] proved that if p(z) eq 0 in the unit disk, then for 0< r≤ 1, _|z|=r|p(z)|≥ (r+12)^n_|z|=1|p(z)|. In this paper, we prove a sharpening and generalization of this result and show by means of examples that for some polynomials our result can significantly improve the bound obtained by the Rivlin's Theorem.