No Jackson-type estimates for piecewise q-monotone, q3, trigonometric approximation

Authors

  • D. Leviatan Raymond and Beverly Sackler School Math. Sci., Tel Aviv Univ., Israel
  • O. V. Motorna Taras Shevchenko Nat. Univ. Kyiv, Ukraine
  • I. A. Shevchuk Taras Shevchenko Nat. Univ. Kyiv, Ukraine

DOI:

https://doi.org/10.37863/umzh.v74i5.7081

Keywords:

iecewise q-monotone functions, Co-q-monotone trigonometric approximation, Degree of approximation

Abstract

UDC 517.5

We say that a function fC[a,b] is q-monotone, q3, if fCq2(a,b) and f(q2) is convex in (a,b). Let f be continuous and 2π-periodic, and change its q-monotonicity finitely many times in [π,π]. We are interested in estimating the degree of approximation of f by trigonometric polynomials which are co-q-monotone with it, namely, trigonometric polynomials that change their q-monotonicity exactly at the points where f does. Such Jackson type estimates are valid for piecewise monotone (q=1) and piecewise convex (q=2) approximations. However, we prove, that no such estimates are valid, in general, for co-q-monotone approximation, when q3.

Author Biography

  • O. V. Motorna, Taras Shevchenko Nat. Univ. Kyiv, Ukraine

     

     

References

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Published

17.06.2022

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Section

Research articles

How to Cite

Leviatan , D., et al. “No Jackson-Type Estimates for Piecewise q-Monotone, q3, Trigonometric Approximation”. Ukrains’kyi Matematychnyi Zhurnal, vol. 74, no. 5, June 2022, pp. 662-75, https://doi.org/10.37863/umzh.v74i5.7081.