Abstract
We discuss the behaviour of the Θ-means of Walsh series of a function in Lp (1 ≤ p ≤ ∞). We investigate the rate of the approximation by this means, in particular, in Lip(α, p), where α > 0 and 1 ≤ p ≤ ∞. In case p = ∞ by Lp we mean C, the class of the continuous functions.
Our main theorems give a common generalization of two results of Móricz and Siddiqi on Nörlund means [11] and Móricz and Rhoades on weighted means [9].
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Blahota, I., Nagy, K. Approximation by Θ-Means of Walsh–Fourier Series. Anal Math 44, 57–71 (2018). https://doi.org/10.1007/s10476-018-0106-3
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DOI: https://doi.org/10.1007/s10476-018-0106-3
Key words and phrases
- Walsh group
- Walsh system
- Walsh–Fourier series
- Nörlund mean
- weighted mean
- approximation
- modulus of continuity
- Lipschitz function
- Θ-mean