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<p>We introduce a new class of functions, namely, the generalized Zygmund class with weight. Moreover, we determine the degree of approximation for functions belonging to this class. The degree of approximation is expressed in terms of two moduli of continuity of the second order <i>w</i><sub>1</sub> and <i>w</i><sub>2</sub> such that <i>w</i><sub>1</sub><i>/w</i><sub>2</sub> is positive and nondecreasing. To realize this task, for approximation we use the even-type delayed mean of their Fourier series.</p>

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Application of the Even-Type Delayed Mean in the Approximation of Functions from the Generalized Zygmund Class with Weight

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • Xhevat Z. Krasniqi

摘要

We introduce a new class of functions, namely, the generalized Zygmund class with weight. Moreover, we determine the degree of approximation for functions belonging to this class. The degree of approximation is expressed in terms of two moduli of continuity of the second order w1 and w2 such that w1/w2 is positive and nondecreasing. To realize this task, for approximation we use the even-type delayed mean of their Fourier series.