Author/Authors :
Malik, S.A Department of Mathematics - University of Kashmir - Srinagar, India , Zargar, B.A Department of Mathematics - University of Kashmir - Srinagar, India , Zargar, F.A Department of Mathematics - University of Kashmir - Srinagar, India , Sofi, F.A Department of Mathematics - Govt. College for Women - M.A. Road - Srinagar, India
Abstract :
Let p(z) =
Σn
v=0
avzv be a polynomial of degree n. Let p′(z) and Dαp(z) = np(z)+(α−z)p′(z) be the
ordinary and polar derivative of p(z) respectively. In this paper some sharp lower bound estimates
for the maximal modulus of p′(z) and Dαp(z) are established in terms of their degrees, coefficients
and maximal modulus of p(z) over unit disk under the assumption that all the zeros of p(z) lie in
|z| ≤ k, k ≥ 1.
Keywords :
Lower bound , Maximum modulus , Polar derivative , Polynomial
