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Research Paper | Mathematics | India | Volume 12 Issue 11, November 2023
Degree of Approximation in Generalized Zygmund Class Using (N, Pn) (E, 1) Means of Fourier Series
Abstract: This article delves into the theory of summability, specifically focusing on the generalization of the limit concept for sequences and series influenced by linear means of sequence or series. Researchers have shown significant interest in exploring the degree of approximation of functions in the Lipschitz and Zygmund classes using various means of Fourier series and conjugate Fourier series. The paper introduces the generalized Zygmund class and investigates the degree of approximation of functions within it using the (N, Pn) (E, 1) means of Fourier series. The article presents a theorem that provides an expression for the degree of approximation in this context. The proof of the theorem involves several lemmas and mathematical techniques. This work contributes to the understanding of approximation theory and the application of Fourier series in generalized Zygmund classes.
Keywords: Degree of approximation, Generalized Zygmund class, (N, Pn) mean , (E, 1) mean, (N, Pn) (E, 1) mean . summability method
Edition: Volume 12 Issue 11, November 2023,
Pages: 1665 - 1668