TY - JOUR AU - S. B. Vakarchuk PY - 2014/06/25 Y2 - 2024/03/28 TI - Jackson-Type Inequalities for the Special Moduli of Continuity on the Entire Real Axis and the Exact Values of Mean $ν$ - Widths for the Classes of Functions in the Space $L_2 (ℝ)$ JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 66 IS - 6 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2175 AB - The exact values of constants are obtained in the space $L_2 (ℝ)$ for the Jackson-type inequalities for special moduli of continuity of the $k$ th order defined by the Steklov operator $S_h (f)$ instead of the translation operator $T_h (f)$ in the case of approximation by entire functions of exponential type $σ ∈ (0,∞)$. The exact values of the mean $ν$-widths (linear, Bernstein, and Kolmogorov) are also obtained for the classes of functions defined by the indicated characteristic of smoothness. ER -