Ukrainian Mathematical Journal

, Volume 57, Issue 2, pp 331–339 | Cite as

Shape-Preserving Smoothing of 3-Convex Splines of Degree 4

  • A. V. Prymak


For every 3-convex piecewise-polynomial function s of degree ≤4 with n equidistant knots on [0, 1] we construct a 3-convex spline s1 (s1C(3)) of degree ≤4 with the same knots that satisfies the inequality
$$\left\| {S - S_1 } \right\|_{C_{[0,1]} } \leqslant c\omega _5 (s;1/n),$$
where c is an absolute constant and ω5 is the modulus of smoothness of the fifth order.


Absolute Constant 
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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • A. V. Prymak
    • 1
  1. 1.Shevchenko Kyiv National UniversityKyivUkraine

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