Abstract
We obtain pointwise estimates for the coconvex approximation of functions of the class W r, r > 3.
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REFERENCES
G. A. Dzyubenko, J. Gilewicz, and I. A. Shevchuk, “Coconvex pointwise approximation,” Ukr. Mat. Zh., 54, No.9, 1200–1212 (2002).
H. A. Dzyubenko and V. D. Zalizko, “Coconvex approximation of functions with more than one inflection point,” Ukr. Mat. Zh., 56, No.3, 352–365 (2004).
M. G. Pleshakov and A. V. Shatalina, “Piecewise coapproximation and the Whitney inequality,” Approxim. Theor., 105, 189–210 (2000).
D. Leviatan and I. A. Shevchuk, “Coconvex approximation,” Approxim. Theor., 118, 20–65 (2002).
K. A. Kopotun, “Pointwise and uniform estimates for convex approximation of functions by algebraic polynomials,” Constr. Approxim., 10, 153–178 (1994).
I. A. Shevchuk, Polynomial Approximation and Traces of Functions Continuous on a Segment [in Russian], Naukova Dumka, Kiev (1992).
A. S. Shvedov, “Orders of coapproximations of functions by algebraic polynomials,” Mat. Zametki, 30, 839–846 (1981).
X. Wu and S. P. Zhou, “A counterexample in comonotone approximation in L p space,” Colloq. Math., 64, 265–274 (1993).
I. A. Shevchuk, “Approximation of monotone functions by monotone polynomials,” Mat. Sb., 183, 63–78 (1992).
G. A. Dzyubenko, J. Gilewicz, and I. A. Shevchuk, “Piecewise monotone pointwise approximation,” Constr. Approxim., 14, 311–348 (1998).
R. A. de Vore, “Monotone approximation by polynomials,” SIAM J. Math. Anal., 8, 906–921 (1977).
V. K. Dzyadyk, Introduction to the Theory of Uniform Approximation of Functions by Polynomials [in Russian], Nauka, Moscow (1977).
R. A. de Vore and X. M. Yu, “Pointwise estimates for monotone polynomial approximation,” Constr. Approxim., 1, 323–331 (1985).
V. K. Dzyadyk, “On the constructive characteristic of functions satisfying the condition (Lip α (0 < α < 1)) on a finite segment of the real axis,” Izv. Akad. Nauk SSSR, Ser. Mat., 20, No.2, 623–642 (1956).
H. Whitney, “On functions with bounded nth differences,” J. Math. Pures Appl., 8, No.36, 67–95 (1957).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 1, pp. 47–59, January, 2005.
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Dzyubenko, H.A., Zalizko, V.D. Pointwise Estimates for the Coconvex Approximation of Differentiable Functions. Ukr Math J 57, 52–69 (2005). https://doi.org/10.1007/s11253-005-0171-1
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DOI: https://doi.org/10.1007/s11253-005-0171-1