Properties and approximation of integrable functions

V.P. Motornyi (Oles Honchar Dnipropetrovsk National University)
U.P. Babyak (Oles Honchar Dnipropetrovsk National University)
K.R. Studenikina (Oles Honchar Dnipropetrovsk National University)
M.V. Shtats'ka (Oles Honchar Dnipropetrovsk National University)

Abstract


Some properties of the functions integrable on the segment were considered in this article. Estimates for approximation are obtained.

Keywords


modulus of continuity; integral; function

References


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Ul'yanov P.L. "On series by Haar system", Matem. sbornik, 1964; 63(3): pp. 356-391. (in Russian)

Ul'yanov P.L. "Inclusion of certain classes $$$H_p^{\omega}$$$ of functions", Izvestiya AN USSR. Ser. matem., 1968; 32(3): pp. 649-686. (in Russian) doi:10.1070/IM1968v002n03ABEH000650

Timan A.F. Approximation theory for real-variable functions, Fizmatgiz, Moscow, 1960; 624 p. (in Russian)

Khodak L.B. Some problems of approximation of non-periodic functions by algebraic polynomials: Diss. Cand. Phys.-Math. Sc., Dnipropetrovsk, 1979; 108 p. (in Russian)

Motornyi V.P., Klimenko M.S. "Mean approximation of functions by algebraic polynomials", Res. Math., 2012; 17: pp. 106-117. (in Ukrainian) doi:10.15421/241215




DOI: https://doi.org/10.15421/241707

  

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Copyright (c) 2017 V.P. Motornyi, U.P. Babyak, K.R. Studenikina, M.V. Shtats'ka

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