Sharp inequality of Jackson–Stechkin type and widths of functional classes in the space \( L_2 \)

Abstract

For classes of differentiable periodic functions, defined by means of generalized moduli of continuity \( \Omega_m(f, t) \), satisfying the condition \( \left( \int_0^h \Omega_m^{2/m}(f(r), t)\,dt \right)^{m/2} \leq \Phi(h) \), where \( m \in \mathbb{N} \), \( r \in \mathbb{Z}_+ \), \( h > 0 \) and \( \Phi \) is a given majorant, under certain restrictions on the majorant, the exact values of various \( n \)-widths in the space \( L_2 \) are calculated.