Estimates of approximative characteristics of the classes $B^{\Omega}_{p,\theta}$ of periodic functions of several variables with given majorant of mixed moduli of continuity in the space $L_{q}$

O. Fedunyk-Yaremchuk, S. Hembars'ka

Abstract


In this paper, we continue the study of approximative characteristics of the classes $B^{\Omega}_{p,\theta}$ 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 $B^{\Omega}_{p,\theta}$in the space $L_{q},$ $1\leq p<q<\infty,$ and also establish the exact-order estimates of approximation for these classes of functions in the space $L_{q}$ by using linear operators satisfying certain conditions.

Keywords


orthoprojective width, mixed modulus of continuity, linear operator, Vall\'{e}e-Poussin kernel, Fej\'{e}r kernel

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