Exact constants in Jackson-type inequalities and exact values of the widths of some classes of functions in \(L_{2}\)
The authors find the exact values of the \(n\)-widths for the classes of periodic differentiable functions in \(L_2[0,2\pi]\) satisfying the constraint \[ \int^h_0 t\widetilde\Omega^{1/m}_m(f^{r}; t)\,dt\leq \Phi(h), \] where \(h> 0\), \(m\in\mathbb{N}\), \(r\in\mathbb{Z}_+\), \(\widetilde\Omega_m^{1/m}(f^{r}; t)\) is the generalized \(m\)th-order continuity modulus of the derivative \(f^{(r)}\in L_1[0,2\pi]\), while \(\Phi(t)\) is an arbitrary increasing function such that \(\Phi(0)= 0\).
scientific article; zbMATH DE number 6009108
scientific article