On the location of zeros of generalized derivative
INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS(2022)
摘要
Let P(z) = Pi(n)(v=1) (z - z(v)), be a monic polynomial of degree n, then, G gamma inverted right perpendicularP(z)inverted left perpendicular = Sigma(n)(k=1) gamma k Pi(n)(v=1,v not equal k) (z - z(v)), where gamma = (gamma(1), gamma(2), ..., gamma(n)) is a n-tuple of positive real numbers with Sigma(n)(k=1) gamma k = 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.
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关键词
polynomial, zeros, critical points, derivative, generalized derivative
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