Nearly monotone spline approximation in double struck L signp

K. Kopotun, D. Leviatan, A. V. Prymak

Research output: Contribution to journalArticlepeer-review


It is shown that the rate of Lp-approximation of a non-decreasing function in double struck L signp, 0 < p < oc, by "nearly non-decreasing" splines can be estimated in terms of the third classical modulus of smoothness (for uniformly spaced knots) and third Ditzian-Totik modulus (for Chebyshev knots), and that estimates in terms of higher moduli are impossible. It is known that these estimates are no longer true for "purely" monotone spline approximation, and properties of intervals where the monotonicity restriction can be relaxed in order to achieve better approximation rate are investigated.

Original languageEnglish
Pages (from-to)2037-2047
Number of pages11
JournalProceedings of the American Mathematical Society
Issue number7
StatePublished - Jul 2006


  • Degree of approximation
  • Jackson type estimates
  • Monotone approximation by piecewise polynomials and splines


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