Abstract

We shall give an account of some of the fundamental results concerning critical points of polynomials as well as some of the developments concerning extremal properties of polynomials with an analysis of some inequalities for polynomials and their derivatives as well as their zeros. We provide a counterexample to a theorem of M. Marden concerning the zeros of certain composite polynomials.KeywordsUnit DiskExtremal ProblemChebyshev PolynomialTrigonometric PolynomialUnit DistanceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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