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

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 $L_M(\mathbb{R}^n)$. For this purpose, we use a special scale of approximation spaces $\mathcal{B}_\tau^s(M)$ that are interpolation spaces between the subspace $\mathscr{E}_M$ of exponential type functions and the space $L_M(\mathbb{R}^n)$. These approximation spaces are defined using a functional $E\left(t,f\right)$ that plays a similar role as the module of smoothness. The constants in obtained inequalities are expressed using a normalization factor $N_{\vartheta,q}$ that is determined by the parameters $\tau$ and $s$ of the approximation space $\mathcal{B}_\tau^s(M)$.

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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 (2), 364-370.