An Upper bound of a derivative for some class of polynomials

Abstract

.], Kumar and Lal provided an upper bound of a derivative for polynomial degree n having some of zeros at the origin and rest of zeros lying on or outside the boundary of a prescribed disk. In this paper, we present an upper bound of a derivativen having zeros z 0 ,... ,z m with |z j | < 1 for 0 j m and the remaining n − (t m + ··· +t 0 ) zeros are outside {z : |z| < k} where k 1.Mathematics subject classification (2010): 30A10, 30C10, 30C15.

L^r inequalities for polynomials with restricted zeros

“…Nakprasit and Somsuwan [16] proved a generalization and improvement of inequality (1.10) by considering polynomials having a zero of order s at a point in the disc |z| < 1 and the rest of the zeros are in |z| ≥ k, k ≥ 1. In fact, they obtained…”