Growth of a polynomial with restricted zeros

In this paper, we establish some upper bound estimates for the maximal modulus of a polynomial on a disk |z|=R,R≥1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|z|=R, \,R\ge 1$$\end{document}, when there is a restriction on its zeros. The obtained results generalize as well as sharpen some already known estimates due to Govil, Dalal and Govil, Dewan and Bhat and the classical result of Ankeny and Rivlin.