APPROXIMATION PROBLEMS ON THE SMOOTHNESS CLASSES

This paper investigates the relative Kolmogorov n-widths of 2π-periodic smooth classes in ■.We estimate the relative widths of ■ and its generalized class KpHω（Pτ）,where KpHω（Pτ） is defined by a self-conjugate differential operator Pτ（D） induced by ■,tj>0,j=1,2,…,l,l≥1,σ≥1,r=2l+σ.Also,the modulus of continuity of the τ-th derivative,or τ-th self-conjugate differential,does not exceed a given modulus of continuity ω.Then we obtain the asymptotic results,especially for the case p=∞,1≤q≤∞.