TY - JOUR
AU - S. B. Vakarchuk
PY - 2019/02/25
Y2 - 2022/10/05
TI - On the estimates of widths of the classes of functions defined by the generalized
moduli of continuity and majorants in the weighted space $L_{2x} (0,1)$
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 71
IS - 2
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/1430
AB - The upper and lower estimates for the Kolmogorov, linear, Bernstein, Gelfand, projective, and Fourier widths are obtainedin the space $L_{2,x}(0, 1)$ for the classes of functions $W^r_2 (\Omega^{(
u )}_{m,x}; \Psi )$, where $r \in Z+, m \in N,
u \geq 0,$ and $\\Omega^{(
u )}_{m,x}$ and $\Psi$ are the mth order generalized modulus of continuity and the majorant, respectively. The upper and lower estimates forthe suprema of Fourier – Bessel coefficients were also found on these classes. We also present the conditions for majorantsunder which it is possible to find the exact values of indicated widths and the suprema of Fourier – Bessel coefficients.
ER -