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((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).

published proceedings

  • JOURNAL OF APPROXIMATION THEORY

author list (cited authors)

  • Erdelyi, T.

citation count

  • 5

complete list of authors

  • Erdélyi, Tamás

publication date

  • April 2015