Weighted Turán type inequality for the derivative of real algebraic polynomials which have complex zeros

Dejun Zhao, Zihou Zhang

Abstract


In this paper, we establish a weighted Turán  type inequality with N-doubling weights for the polynomials of degree at most n with real coefficients that have at most  r complex zeros, which r is a fixed positive integer  and n is sufficiently large. This result gives a partial answer to an open problem in [11].


Keywords


Real algebraic polynomial, Turán type inequality, Complex zero, Generalized doubling weights.

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References


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