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 $L_{q}$

Keywords: orthoprojective width, mixed modulus of continuity, linear operator, Vallée-Poussin kernel, Fejér kernel
Published online: 2019-12-31

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.

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How to Cite
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Fedunyk-YaremchukO., Hembars’kaS. 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 $L_{q}$. Carpathian Math. Publ. 2019, 11 (2), 281-295.