SOME INTEGRAL MEAN ESTIMATES FOR POLYNOMIALS

N Rather, Suhail Gulzar, K Thakur
2014 NEW ZEALAND JOURNAL OF MATHEMATICS   unpublished
For the class of Lacunary polynomials P (z) = anz n + n ν=µ a n−ν z n−ν , 1 ≤ µ ≤ n, of degree n having all their zeros in |z| ≤ k where k ≤ 1, Aziz and Shah [6] proved for each r > 0 n 2π 0 P e iθ r dθ 1 r ≤ 2π 0 1 + k µ e iθ r dθ 1 r max |z|=1 |P (z)|. In this paper, we extend above inequality to the polar derivative thereby establish some refinements and generalizations of some known polynomial inequalities concerning the polar derivative of a polynomial with restricted zeros.
fatcat:owyadcnt2rhnbnvthuvxxpdgvy