(untitled) (Analysis in Theory and Applications, 2011)
If p(z) is a polynomial of degree n having all its zeros on |z| = k, k ≤ 1, then it is proved[5] that _|z|=1|p′(z)| ≤nk^n−1+k^n_|z|=1|p(z)|.In this paper, we generalize the above inequality by extending it to the polar derivative of a polynomial of the type p(z) = c_nz^n +_j=μ^nc_n-jz^n-j, 1 ≤ μ ≤ n. We also obtain certain new inequalities concerning the maximum modulus of a polynomial with restricted zeros.