On approximation by trigonometrical polynomials in $$$L_2$$$ space

O.V. Polyakov (Oles Honchar Dnipropetrovsk National University)

Abstract


We obtain certain inequalities of Jackson type, connecting the value of the best approximation of periodic differentiable functions and the generalized modulus of continuity of the highest derivative.

Keywords


best approximation; modulus of continuity

References


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

Chernykh N.I. "On Jackson inequalities in $$$L_2$$$ space", Trudy MIAN SSSR, 1967; 88: pp. 71-74. (in Russian)

Ligun A.A. "Some inequalities between the best approximation and the modulus of continuity in $$$L_2$$$ space", Matem. zametki, 1978; 24(6): pp. 785-792. (in Russian)

Doronin V.G., Ligun A.A. "Exact constant in Jackson inequality in $$$L_2$$$ space", Ukrainian Math. J., 1994; 46(9): pp. 1261-1265. (in Russian)

Shalaev V.V. "On widths in $$$L_2$$$ of classes of differentiable functions, defined by moduli of continuity of the highest orders", Ukrainian Math. J., 1991; 43(1): pp. 125-129. (in Russian)

Vakarchuk S.B., Zabutnaya V.I. "Inequalities of Jackson-Stechkin type for special moduli of continuity and widths of functional classes in $$$L_2$$$", Matem. zametki, 2012; 92(4): pp. 497-514. (in Russian)

Abilov V.A., Abilova F.V. "Some problems of approximation of $$$2\pi$$$-periodic functions by Fourier sums in $$$L_2(2\pi)$$$ space", Matem. zametki, 2004; 76(6): pp. 803-811. (in Russian)

Vakarchuk S.B. "Exact constants in inequalities of Jackson type and exact values of widths of functional classes from $$$L_2$$$", Matem. zametki, 2006; 78(5): pp. 11-19. (in Russian)

Vakarchuk S.B. "Generalised characteristics of smoothness in inequalities of Jackson type and widths of classes of functions in $$$L_2$$$", Matem. zametki, 2015; 98(4): pp. 511-529. (in Russian)

Shalaev V.V. "On one estimate of approximation of differentiable functions by trigonometrical polynomials", Researches on modern problems of summation and approximation of functions and their applications, Dnipropetrovsk, 1979; pp. 39-43 (in Russian)




DOI: https://dx.doi.org/10.15421/241614

  

Refbacks

  • There are currently no refbacks.


Copyright (c) 2016 O.V. Polyakov

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


Registered in


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