TURAN-TYPE INEQUALITIES OF POLYNOMIALS

If p(z) = Sigma(n)(v=0) a(nu)z(nu) is a polynomial of degree n having all its zeros in |z| <= k, k >= 1, V. K. Jain [Bull. Math. Soc. Sci. Math. Roum., Nouv. Ser. 59 (2016), 339-347] proved max(|z|=1) |p'(z)| >= n(|a(0)| + |a(n)|k(n+1))/|a(o)| (1 + k(n+1)) + |a(n)| (k(n+1) + k(2n)) max(|z|=1) |p(z)|. We first obtain a generalization as well as improvement of the above inequality. Further, we extend our first result to a more generalized result which yields improved results of some known inequalities as particular case.