### On the nonsymmetric approximation of continuous functions in the integral metric

#### Abstract

Taking into account Babenko's theorem on the connection of nonsymmetric approximation with the usual best approximation in the integral metric and the best one-sided approximations, from the proved result we obtain the exact estimate for the usual best approximation obtained by N.P. Korneichuk, and the exact estimate for the best one-sided approximation obtained by V.G. Doronin and A.A. Ligun.

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PDF#### References

Babenko V.F. "Non-symmetric approximations in spaces of integrable functions", *Ukrainian Math. J.*, 1982; 34(4); pp. 409-416. (in Russian)

Korneichuk N.P. "On widths of classes of continuous functions in $$$L_p$$$ space", *Matem. zametki*, 1971; 10(5); pp. 493-500. (in Russian) doi:10.1007/BF01109031

Korneichuk N.P. *Splines in approximation theory*, Nauka, Moscow, 1984; 544 p. (in Russian)

Khoroshko N.P. "On the best approximation of functions of $$$H_{\omega}[0;1]$$$ class by polynomials by Haar system in $$$L_p$$$ metric", *Researches on modern problems of summation and approximation of functions and their applications*, DGU, Dnipropetrovsk, 1972; pp. 74-76. (in Russian)

Doronin V.G., Ligun A.A. "On the problem of the best approximation of some classes of continuous functions", *Researches on modern problems of summation and approximation of functions and their applications*, DGU, Dnipropetrovsk, 1974; pp. 42-49. (in Russian)

Korneichuk N.P. *Extremum problems in approximation theory*, Moscow, 1976; 320 p. (in Russian)

DOI: https://doi.org/10.15421/241909

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