On the estimates of widths of the classes of functions defined by the generalized moduli of continuity and majorants in the weighted space $L_{2x} (0,1)$

Abstract

The upper and lower estimates for the Kolmogorov, linear, Bernstein, Gelfand, projective, and Fourier widths are obtained in the space $L_{2,x}(0, 1)$ for the classes of functions $W^r_2 (\Omega^{(\nu )}_{m,x}; \Psi )$, where $r \in Z+, m \in N, \nu \geq 0,$ and $\\Omega^{(\nu )}_{m,x}$ and $\Psi$ are the mth order generalized modulus of continuity and the majorant, respectively. The upper and lower estimates for the suprema of Fourier – Bessel coefficients were also found on these classes. We also present the conditions for majorants under which it is possible to find the exact values of indicated widths and the suprema of Fourier – Bessel coefficients.