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


Motornyi V.P. "Approximation of functions by algebraic polynomials in $$$L_p$$$ metric", Izv. AN SSSR. Ser.: Matematika, 1971; 35(4): pp. 874-899. (in Russian)

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)

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

Hodak 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", Dnipr. Univ. Math. Bull., 2012; 17: pp. 106-117. (in Ukrainian)


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