Lγ Inequalities for the Polar Derivative of Polynomials

Abstract

In this paper, firstly, we obtain an inequality in Lγ analogue concerning the polar derivative for a polynomial p(ξ) = Xm ν=0 cνξν of degree m having no zero in |ξ| < r, r ≥ 1 proved by Govil et al. [15]. Secondly, we also prove Lγ version for the polar derivative of an ordinary inequality for a polynomial having all its zeros in |ξ| ≤ r, r ≤ 1 proved in that same paper. Our results generalize and improve some known inequalities.