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

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Abstract

For every 3-convex piecewise-polynomial function s of degree ≤4 with n equidistant knots on [0, 1] we construct a 3-convex spline s 1 (s 1C (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.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 2, pp. 277–283, February, 2005.

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Prymak, A.V. Shape-Preserving Smoothing of 3-Convex Splines of Degree 4. Ukr Math J 57, 331–339 (2005). https://doi.org/10.1007/s11253-005-0193-8

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  • DOI: https://doi.org/10.1007/s11253-005-0193-8

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