Bernstein-Jackson-type inequalities with exact constants in Orlicz spaces

Authors

  • M.I. Dmytryshyn Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine https://orcid.org/0000-0002-3248-7736
  • L.I. Dmytryshyn Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine https://orcid.org/0000-0003-1842-8112
https://doi.org/10.15330/cmp.14.2.364-370

Keywords:

Bernstein and Jackson inequalities, best approximation, Orlicz space
Published online: 2022-09-04

Abstract

We establish the Bernstein and Jackson type inequalities with exact constants for estimations of best approximations by exponential type functions in Orlicz spaces LM(Rn). For this purpose, we use a special scale of approximation spaces Bsτ(M) that are interpolation spaces between the subspace EM of exponential type functions and the space LM(Rn). These approximation spaces are defined using a functional E(t,f) that plays a similar role as the module of smoothness. The constants in obtained inequalities are expressed using a normalization factor Nϑ,q that is determined by the parameters τ and s of the approximation space Bsτ(M).

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How to Cite
(1)
Dmytryshyn, M.; Dmytryshyn, L. Bernstein-Jackson-Type Inequalities With Exact Constants in Orlicz Spaces. Carpathian Math. Publ. 2022, 14, 364-370.