on the location of zeros of generalized derivative

Let p(z) = πn v=1 (z − zv), be a monic polynomial of degree n, then, gγ[p(z)] = σn k=1 γk πn v=1,v≠k (z − zv), where γ = (γ1, γ2, . . . , γn) is a n-tuple of positive real numbers with σn k=1 γk = n, be its generalized derivative. the classical gauss-lucas theorem on the location of critical points have been extended to the class of generalized derivative[4]. in this paper, we extend the specht theorem and the results proved by a.aziz [1] on the location of critical points to the class of generalized derivative.