In this paper we consider for a fixed \mu, the class of polynomials P(z)=a_0+\sum\limits_{\nu=\mu}^{n}a_\nu z_\nu,\, 1\leq \mu \leq n, of degree at most n not vanishing in the disk |z|<k, k>0. For any \rho>\sigma\geq 1 and 0<r\leq R\leq k, we investigate the dependence of \parallel P(\rho z)-P(\sigma z)\parallel_R on \parallel P \parallel_r and derive various refinements and generalizations of some well known results.

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  Dawood, Q. M. , Mir, Abdullah