Approximation of classes of periodic functions of several variables with given majorant of mixed moduli of continuity

Keywords:
orthoprojective width, mixed modulus of continuity, linear operator, Vallée-Poussin kernel, Fejér kernelAbstract
In this paper, we continue the study of approximation characteristics of the classes BΩp,θBΩp,θ of periodic functions of several variables whose majorant of the mixed moduli of continuity contains both exponential and logarithmic multipliers. We obtain the exact-order estimates of the orthoprojective widths of the classes BΩp,θBΩp,θ in the space Lq,Lq, 1≤p<q<∞,1≤p<q<∞, and also establish the exact-order estimates of approximation for these classes of functions in the space LqLq by using linear operators satisfying certain conditions.