### Approximation by algebraic polynomials in metric spaces $$$L_{\psi}$$$

#### Abstract

#### Keywords

#### Full Text:

PDF (Русский)#### References

Krein S.G., Petunin Yu.I., Semyonov Ye.M. *Interpolation of linear operators*, Nauka, Moscow, 1978; 400 p. (in Russian)

Storozhenko E.A., Krotov V.G., Osval'd P. "Direct and inverse theorems of Jackson type in $$$L_p$$$ spaces, $$$0 < p < 1$$$", *Mat. sb.*, 1975; 98(3): pp. 395-415. (in Russian) doi:10.1070/SM1975v027n03ABEH002519

Ivanov V.I. "Direct and inverse theorems of approximation theory in the metric of $$$L_p$$$ when $$$0 < p < 1$$$", *Mat. zametki*, 1975; 18(5): pp. 641-658. (in Russian) doi:10.1007/BF01153563

Storozhenko E.A., Osval'd P. "Jackson theorem in $$$L_p({\mathbb{R}}^k)$$$ spaces, $$$0 < p < 1$$$", *Dokl. AN SSSR*, 1976; 229(3): pp. 554-557. (in Russian)

Storozhenko E.A., Osval'd P. "Jackson theorem in $$$L_p({\mathbb{R}}^k)$$$ spaces, $$$0 < p < 1$$$", *Sib. mat. zhurn.*, 1978; 19(4): pp. 888-901. (in Russian)

Pichugov S.A. "On Jackson theorem for periodic functions in spaces with integral metric", *Ukrainian Math. J.*, 2000; 52(1): pp. 122-133. (in Russian) doi:10.1007/BF02514142

Pichugov S.A. "On Jackson theorem for periodic functions in metric spaces with integral metric. II", *Ukrainian Math. J.*, 2011; 63(11): pp. 1524-1533. (in Russian) doi:10.1007/s11253-012-0609-1

Storozhenko E.A. "Approximation by algebraic polynomials in $$$L_p$$$, $$$0 < p < 1$$$", *Vestnik MGU. Seriya: Matematika, Mehanika*, 1978; 4: pp. 87-92. (in Russian)

Khodak L.B. "On approximation of functions by algebraic polynomials in $$$L_p$$$ metric when $$$0 < p < 1$$$", *Mat. zametki*, 1981; 30(3): pp. 321-332. (in Russian) doi:10.1007/BF01141619

Shvedov A.S. "Jackson theorem in $$$L_p$$$, $$$0 < p < 1$$$, for algebraic polynomials, and the orders of comonotone approximations", *Mat. zametki*, 1979; 25(1): pp. 107-117. (in Russian) doi:10.1007/BF01138150

Runovski K. "On Jackson’s type inequalities in Orlicz classes", *Revista Mat. Comp.*, 2001; 14(2): pp. 394-404.

Brudnyi Yu.A. "Approximation of functions by algebraic polynomials", *Izv. AN SSSR*, 1968; 32(4): pp. 780-787. (in Russian)

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

DOI: https://doi.org/10.15421/241301

### Refbacks

- There are currently no refbacks.

Copyright (c) 2013 T.A. Agoshkova

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