Exact Jackson - Stechkin-type inequalities for 2π -periodic functions in L 2 and widths of some classes of functions
We consider the problem of finding exact inequalities for the best approximations of periodical differentiable functions by trigonometric polynomials and the m -order moduli of continuity in the space L 2 and present their applications. For some classes of functions defined by the indicated moduli of continuity, we calculate the exact values of n-widths in the space L 2 .
English version (Springer): Ukrainian Mathematical Journal 63 (2011), no. 10, pp 1633-1639.
Citation Example: Shabozov M. Sh. Exact Jackson - Stechkin-type inequalities for 2π -periodic functions in L 2 and widths of some classes of functions // Ukr. Mat. Zh. - 2011. - 63, № 10. - pp. 1434-1440.