Jackson--Stechkin Type Inequalities for Special Moduli of Continuity and Widths of Function Classes in the Space~$L_2$

S. B. Vakarchuk ; V. I. Zabutnaya

Matematičeskie zametki, Tome 92 (2012) no. 4, pp. 497-514.

Résumé

We obtain sharp Jackson–Stechkin type inequalities for moduli of continuity of $k$th order $\Omega_k$ in which, instead of the shift operator $T_hf$, the Steklov operator $S_h(f)$ is used. Similar smoothness characteristic of functions were studied earlier in papers of Abilov, Abilova, Kokilashvili, and others. For classes of functions defined by these characteristics, we calculate the exact values of certain $n$-widths.

Détail

Keywords: Jackson–Stechkin type inequality, modulus of continuity, Steklov operator $S_h(f)$, $n$-width, Fourier series, Minkowski's inequality.

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