Inequalities for Lorentz polynomials
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2015 Elsevier Inc. We prove a few interesting inequalities for Lorentz polynomials. A highlight of this paper states that the Markov-type inequality maxx[-1,1]|f'(x)|nmaxx[-1,1]|f(x)| holds for all polynomials f of degree at most n with real coefficients for which f' has all its zeros outside the open unit disk. Equality holds only for f(x):=c((1x)n-2n-1) with a constant 0cR. This should be compared with Erdos's classical result stating that maxx[-1,1]|f'(x)|n2(nn-1)n-1maxx[-1,1]|f(x)| for all polynomials f of degree at most n having all their zeros in R{set minus}(-1,1).