Inequalities for Lorentz polynomials Academic Article uri icon

abstract

  • © 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((1±x)n-2n-1) with a constant 0≠c∈R. 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).

author list (cited authors)

  • Erdélyi, T.

citation count

  • 3

publication date

  • April 2015