Some inequalities concerning the rate of growth of polynomials

In this paper we consider a class of polynomials p(z)=a0+\sumlv=tn avzv, t\ge1, not vanishing in |z|
Anahtar Kelimeler:

Polynomial, Zeros, Inequalities.

Some inequalities concerning the rate of growth of polynomials

In this paper we consider a class of polynomials p(z)=a0+\sumlv=tn avzv, t\ge1, not vanishing in |z|

___

  • Inequality, (21) when combined with Lemma 7, gives ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ Rt− 1 Rn− 1 |a0| − m kt+1+ 1 ⎭ ⎪⎪ ≤ (Rn− 1) max|p(z)| − m |z|=1 from which the theorem follows.