Let P(z) be a polynomial of degree n having all its zeros in |z| ≤ 1 then for all (αi)t i=1 ∈ C with |αi| ≥ 1,1 ≤ i ≤t < n , it was proved by Jain[V. K. Jain, Generalization of an inequality involving maximum moduli of a polynomial and its polar derivative, Bull Math Soc Sci Math Roum Tome. 98, 6774 (2007)] that max |z|=1|Dαt...Dα2Dα1P(z)|≥ nt 2t"Aαt max |z|=1|P(z)|+ 2t t Y i=1 |αi|−Aαt!min |z|=1|P(z)|#. where nt = n(n − 1)...(n − t + 1) and Aαt = (|α1|− 1)(|α2|− 1)...(|αt|−1).
Gulzar, M., Zargar, B., Akhter, R. (2020). SOME INEQUALITIES FOR THE POLAR DERIVATIVE OF A POLYNOMIAL HAVING S-FOLD ZEROS AT THE ORIGIN.. Communications in Nonlinear Analysis, 8(1), 1-18.
MLA
M H Gulzar; Bashir Ahmad Zargar; Rubia Akhter. "SOME INEQUALITIES FOR THE POLAR DERIVATIVE OF A POLYNOMIAL HAVING S-FOLD ZEROS AT THE ORIGIN.". Communications in Nonlinear Analysis, 8, 1, 2020, 1-18.
HARVARD
Gulzar, M., Zargar, B., Akhter, R. (2020). 'SOME INEQUALITIES FOR THE POLAR DERIVATIVE OF A POLYNOMIAL HAVING S-FOLD ZEROS AT THE ORIGIN.', Communications in Nonlinear Analysis, 8(1), pp. 1-18.
VANCOUVER
Gulzar, M., Zargar, B., Akhter, R. SOME INEQUALITIES FOR THE POLAR DERIVATIVE OF A POLYNOMIAL HAVING S-FOLD ZEROS AT THE ORIGIN.. Communications in Nonlinear Analysis, 2020; 8(1): 1-18.
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