A New Generalization of Jensen's Theorem on the Zeros of the Derivative of a Polynomial

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Let p(z) be a real polynomial all of whose zeros lie in the closed interior of the circle whose diameter is the segment alpha beta of the axis of reals, and let all the non-real zeros lie interior to that circle. For each pair z sub k, conjugate z sub k of conjugate imaginary zeros of p(z) let gamma z sub k be the circle tangent at z sub k and conjugate z sub k to the respective circles alpha z sub k beta and alpha conjugate z sub k beta. Then all non-real zeros of p prime (z) lie in the closed interiors of the gamma sub k. (Author).