Averaged characteristics of smoothness in L_2 and estimations for the widths values of function classes
UDC 517.5 In the space of 2π-periodic functions L_2, we investigate the characteristic of smoothness ω^*_M (f,t):= (1/t) olimits_0^t ω_M (f,τ) d τ obtained as a result of averaging of the generalized modulus of continuity ω_M (f) formed by using a generalized finite-difference operator Δ^M _h L_2 → L_2. We also study some properties of the functions ω_M (f) and ω^*_M (f). For the classes of functions W(ω^*_M , Φ), where Φ is a majorant, we determine the lower and upper estimates for the values of a series of n-widths and the establish the condition for Φ under which we obtain the exact values of these estimates. Several exact results are illustrated by specific examples. , number=2, journal=Ukrains’kyi Matematychnyi Zhurnal, author=Vakarchuk, S. and Zabutna , V. and Vakarchuk, M., year=2025, month=Nov., pages=83–106