New Inequalities on $L_{γ}$-Spaces (Analysis in Theory and Applications, 2013)
We consider for a fixed $μ$, the class of polynomials $$P_{n,μ,s}:=\Bigg\{ P(z) =z^s(a_nz^{n−s}+\sum^{n-s}_{j=μ}a_{n−j}z^{n−j−s}); 1≤μ≤n−s\Bigg\}$$ of degree $n$, having all zeros in $|z|≤k,$ $k≤1$, with $s$-fold zeros at the origin. In this paper,we have obtained inequalities in the reverse direction for the above class of polynomials.Besides, extensions of some Turan-type inequalities for the polar derivative ofpolynomials have been considered.