Approximation of functions by linear methods in weighted Orlicz type spaces with variable exponent

S.O. Chaichenko; A.L. Shidlich

doi:10.15421/242420

Approximation of functions by linear methods in weighted Orlicz type spaces with variable exponent

S.O. Chaichenko (Donbas State Pedagogical University), https://orcid.org/0000-0002-2724-8749
A.L. Shidlich (Institute of Mathematics of the NAS of Ukraine, National University of Life and Environmental Sciences of Ukraine), https://orcid.org/0000-0002-6421-9277

Abstract

The approximation properties of various classical methods of linear summation of Fourier series in weighted spaces of Orlicz type with variable exponent are considered. In particular, in terms of approximation by such methods the constructive characterizations for classes of functions whose moduli of smoothness do not exceed some majorant are obtained.

Keywords

direct approximation theorem; inverse approximation theorem; modulus of smoothness; spaces with variable exponent; Zygmund means; Abel-Poisson means; Taylor-Abel-Poisson means; de la Vallée Poussin means

MSC 2020

41A65; 26A15; 41A25

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References

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