Geodesic
Approximation by linear means of Fourier series and realization functionals in weighted Orlicz spaces
Problemy analiza, Tome 11 (2022) no. 2, pp. 106-118.

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Using one-sided Steklov means, we introduce a new modulus of smoothness in weighted Orlicz spaces and state its equivalence with a special $K$-functional. We prove Stechkin-Nikol'skii-type inequality for trigonometric polynomials and direct estimates for the approximation by Riesz-Zygmund, Vallée-Poussin, and Euler means in weighted Orlicz spaces. By these results, several types of realization functionals equivalent to the above cited $K$-functional in points $1/n$, $n\in\mathbb N$, are constructed.
Keywords: weighted Orlicz spaces, $K$-functional, realization functional, Riesz-Zygmund means, Euler means. 
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S. S. Volosivets. Approximation by linear means of Fourier series and realization functionals in weighted Orlicz spaces. Problemy analiza, Tome 11 (2022) no. 2, pp. 106-118. http://geodesic.mathdoc.fr/item/PA_2022_11_2_a7/

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