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

MSC 2020


41A10; 41A50; 41A29; 26A33

References


Nikolsky S.M. "On the best approximation of functions satisfying Lipschitz condition", Izv. AN SSSR. Ser. Matemat., 1946; 10(4): pp. 295-332. (in Russian)

Temlyakov V.N. "Approximation of functions from the class $$$W^1_{\infty}$$$ by algebraic polynomials", Matem. zametki, 1981; 29(4): pp. 597-602. (in Russian) doi:10.1007/BF01343540

Trigub R.M. "Direct theorems on approximation of smooth functions by algebraic polynomials on the interval", Matem. zametki, 1993; 54(6): pp. 113-121. (in Russian) doi:10.1007/BF01209088

Motornyi V.P. "On exact estimates of pointwise approximation of classes $$$W^r H^{\omega}$$$ by algebraic polynomials", Ukrainian Math. J., 2001; 53(6): pp. 783-799. (in Russian) doi:10.1023/A:1013399801684

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

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)

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. "The best one-sided approximation of classes of fractional integrals with regard to point location on the interval", Res. Math., 2010; 15: pp. 128-132. (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)




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

  

Refbacks

  • There are currently no refbacks.


Copyright (c) 2018 A.M. Pas'ko, V.D. Stefura

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


Registered in

More►


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