Pointwise estimates of the best one-sided approximations of classes $$$W^r_{\infty}$$$ for $$$0 < r < 1$$$

A.M. Pas'ko (Oles Honchar Dnipro National University)
V.D. Stefura (Oles Honchar Dnipro National University)

Abstract


The asymptotic pointwise estimation of the best one-sided approximations to the classes $$$W^r_{\infty}$$$, $$$0 < r < 1$$$, has been established.

Keywords


the best approximation; the best one-sided approximation; asymptotic estimation; pointwise approximation; fractional integral

References


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

Doronin V.G., Ligun A.A. "On the best one-sided approximation on the interval", Izv. vuzov, Matemat., 1980; 5: pp. 16-21. (in Russian)

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

Pas'ko A.M. "The best one-sided approximation of classes of fractional integrals with regard to point location on the interval", Dnipr. Univ. Math. Bull., 2010; 15: pp. 128-132. (in Russian)

Pas'ko A.M. "One-sided approximation of functions with regard to point location on the interval", Dnipr. Univ. Math. Bull., 2005; 10: pp. 86-91. (in Russian)




DOI: https://dx.doi.org/10.15421/241808

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ISSN (Online): 2518-7996
ISSN (Print): 2312-9557