Inequalities for a class of composite polynomials

Abstract

In this paper, we establish some inequalities for a more general class of polynomials P(S(z)), where P(z) = ∑ a_jz^j and S(z) = ∑ b_jz^j of degree n and m respectively. These results not only generalize the results due to Dubinin [ J. Math. Sci., 143 (2007), 3069-3076] but also refine a result due to Shah and Liman [ NFAA, 9(2004), 223-232].