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<p>Direct and inverse theorems of approximation in Orlicz-Stepanets spaces are given in two forms: for modulus of continuity defined by a generalized translation and <i>K</i>-functional of arbitrary order defined by a generalized derivative. Several equivalence theorems connected with an above modulus of continuity or <i>K</i>-functional and Riesz-Zygmund means of Vilenkin-Fourier series are obtained.</p>

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APPROXIMATION IN ORLICZ-STEPANETS SPACES DEFINED BY VILENKIN-FOURIER COEFFICIENTS

  • 期刊论文

  • 发表日期：

    2025年5月1日

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  • Sergey Volosivets

摘要

Direct and inverse theorems of approximation in Orlicz-Stepanets spaces are given in two forms: for modulus of continuity defined by a generalized translation and K-functional of arbitrary order defined by a generalized derivative. Several equivalence theorems connected with an above modulus of continuity or K-functional and Riesz-Zygmund means of Vilenkin-Fourier series are obtained.