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

V.P. Motornyi; V.V. Sedunova

doi:10.15421/241216

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

Full Text:

PDF (Українська)

References

Korneichuk N.P., Ligun A.A., Doronin V.G. Approximation with constraints, Kyiv, 1982; 250 p. (in Ukrainian)

Motornyi V.P., Motornaya O.V. "Comparison theorems for certain non-symmetric classes of functions", Res. Math., 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)

Szego G. Orthogonal polynomials, Amer. Math. Soc. Colloq. Publ. vol. XXIII, Amer. Math. Soc, New York, 1959; Russian transl.: GIFML, Moscow, 1962.

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.