Interpolatory pointwise estimates for polynomial approximation

H. H. Gonska*, D. Leviatan, I. A. Shevchuk, H. J. Wenz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We discuss whether or not it is possible to have interpolatory pointwise estimates in the approximation of a function f ∈ C[0, 1], by polynomials. For the sake of completeness, as well as in order to strengthen some existing results, we discuss briefly the situation in unconstrained approximation. Then we deal with positive and monotone constraints where we show exactly when such interpolatory estimates are achievable by proving affirmative results and by providing the necessary counterexamples in all other cases.

Original languageEnglish
Pages (from-to)603-629
Number of pages27
JournalConstructive Approximation
Issue number4
StatePublished - 2000


  • Approximation by polynomials
  • Degree of approximation
  • Interpolatory pointwise estimates
  • Shape-preserving approximation


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