Integral mean estimates for polar derivative of polynomials.

Let <italic>p</italic>(<italic>z</italic>) be a polynomial of degree <italic>n,</italic> and <italic>D</italic>α<italic>p</italic>(<italic>z</italic>) be its polar derivative of <italic>p</italic>(<italic>z</italic>). Dewan et al proved that if <italic>p</italic>(<italic>z</italic>) has all its zeros in | <italic>z</italic> |≤ <italic>k</italic>, (<italic>k</italic> ≤ 1), with <italic>s</italic> -fold zeros at the origin then for every α ∈ ℂ with | α |≥ <italic>k</italic> and for each <italic>r</italic> >0,<inline-graphic></inline-graphic>In this paper, we obtain a refinement for above inequality. Also we extend some in-equalities for a polynomial of the form <inline-graphic></inline-graphic>. [ABSTRACT FROM AUTHOR]