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)


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


modulus of continuity; integral; function


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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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