Exact Jackson - Stechkin-type inequalities for 2π -periodic functions in <i>L </i>₂ and widths of some classes of functions

Abstract

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