TY - JOUR AU - S. B. Vakarchuk AU - V. G. Doronin PY - 2010/08/25 Y2 - 2024/03/28 TI - Best mean square approximations by entire functions of finite degree on a straight line and exact values of mean widths of functional classes JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 62 IS - 8 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2935 AB - We obtain exact Jackson-type inequalities in the case of the best mean square approximation by entire functions of finite degree $≤ σ$ on a straight line. For classes of functions defined via majorants of averaged smoothness characteristics $Ω_1(f, t ),\; t > 0$, we determine the exact values of the Kolmogorov mean ν-width, linear mean ν-width, and Bernstein mean $ν$-width, $ν > 0$. ER -