The best one-side approximation of classes of integrals of fractional order with regard to position of point on interval

A.M. Pasko

doi:10.15421/241015

The best one-side approximation of classes of integrals of fractional order with regard to position of point on interval

A.M. Pasko (Oles Honchar Dnipropetrovsk National University)

Abstract

We obtain the asymptotic estimations for the best one-sided point-wise approximation to the classes $$$W_{\infty}^r$$$, $$$r > 1$$$ (in case of fractional $$$r$$$) by algebraic polynomials.

Keywords

the best approximation; asymptotic estimation; algebraic polynomial; function class

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References

Motornyi V.P. "Approximation of fractional integrals by algebraic polynomials II", Ukrainian Math. J., 1999; 51(7): pp. 940-951. (in Russian) doi:10.1007/BF02592041

Pasko A.M. "One-sided approximation of functions of the class $$$W^r_{\infty}$$$ by algebraic polynomials with regard to point location on the interval", Res. Math., 2006; 11: pp. 67-70. (in Russian)

Pasko A.M. "One-sided approximation of functions with regard to point location on the interval", Res. Math., 2005; 10: pp. 86-91. (in Russian)

Pasko A.M. "The best one-sided approximation of classes $$$WH^{\omega}$$$ with regard to point location on the interval", Res. Math., 2009; 14: pp. 99-102. (in Russian)