Shape-preserving approximation in Lp

D. Leviatan, V. Operstein

Research output: Contribution to journalArticlepeer-review


We prove a direct theorem for shape preserving Lp-approximation, 0<p<∞, in terms of the classical modulus of smoothness w2(f, tp1). This theorem may be regarded as an extension to Lp of the well-known pointwise estimates of the Timan type and their shape-preserving variants of R. DeVore, D. Leviatan, and X. M. Yu. It leads to a characterization of monotone and convex functions in Lipschitz classes (and more general Besov spaces) in terms of their approximation by algebraic polynomials.

Original languageEnglish
Pages (from-to)299-319
Number of pages21
JournalConstructive Approximation
Issue number3
StatePublished - Sep 1995


  • AMS classification: 41A10, 41A25, 41A29
  • Degree of monotone approximation
  • Polynomial approximation in L


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