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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...
In this paper we study the exponential uniform strong approximation of Marcinkiewicz type of two-dimensional Walsh–Kaczmarz–Fourier series. In particular, it is proved that the Marcinkiewicz type of two-dimensional Walsh–Kaczmarz–Fourier series of every continuous function f is uniformly strong summable to the function f exponentially in the power 1/2. Moreover, it is proved that this result is the...
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