The best one-sided approximations of the class of differentiable functions by algebraic polynomials in $$$L_1$$$ space

V.P. Motornyi (Oles Honchar Dnipropetrovsk National University)
V.V. Sedunova (Oles Honchar Dnipropetrovsk National University)

Abstract


The asymptotic meaning of the best one-sided approximation of functions from the class $$$W^1_{\infty}$$$ by algebraic polynomials of degree not greater than $$$n$$$ in $$$L_1$$$ space is calculated here.

Keywords


function; derivative; polynomial; the best one-sided approximation; Bernulli function

References


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Motornyi V.P., Motornaya O.V. "Comparison theorems for certain non-symmetric classes of functions", Dnipr. Univ. Math. Bull., 2006; 11: pp. 46-53. (in Russian)

Motornyi V.P., Motornaya O.V. "The best mean approximation of classes of differentiable functions by algebraic polynomials", Works of V.A. Steklov mathem. institute. Function theory and differential equations, Moscow, 1995; pp. 171-188. (in Russian)

Natanson I.P. Constructive function theory, FM, Moscow, 1949; 688 p. (in Russian)

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Motornyi V.P., Pas’ko A.N. "On the best one-sided approximation of some classes of differentiable functions in $$$L_1$$$", East J. Approx., 2004; 10(1-2): pp. 159-169.




DOI: https://dx.doi.org/10.15421/241216

  

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Copyright (c) 2012 V.P. Motornyi, V.V. Sedunova

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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
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