Convex Polynomial Approximation in Lp (0 < p < 1) Academic Article uri icon


  • We prove that for each convex function Lp, 0 < p 1, there exists a convex algebraic polynomial Pn of degree n such that [Formula presented] where 2(, t)p is the Ditzian-Totik modulus of smoothness of f(hook) in Lp, and C depends only on p. Moreover, if is also nondecreasing, then the polynomial Pn can also be taken to be nondecreasing, thus we have simultaneous monotone and convex approximation in this case. 1993 Academic Press, Inc.

published proceedings

  • Journal of Approximation Theory

author list (cited authors)

  • Devore, R. A., & Leviatan, D.

citation count

  • 2

complete list of authors

  • Devore, RA||Leviatan, D

publication date

  • January 1993