In this paper we present some results on summability of oneand multi-dimensional Walsh-, Walsh-Kaczmarzand Vilenkin-Fourier series and on the dyadic and Vilenkin derivative. The Fejér and Cesàro summability methods are investigated. We will prove that the maximal operator of the summability means is bounded from the martingale Hardy space Hp to Lp (p > p0). For p = 1 we obtain a weak type inequ...

A general theorem is proved which deduces from a Tauberian condition Ti for a summability method, Tauberian condition Ti for the summability method. Recent results of MeyerKönig and Tietz and of Stieglitz are special cases.

In the present paper, a general theorem on | N̄ , pn |k summability factors of infinite series has been proved under more weaker conditions. Also we have obtained a new result concerning the | C, 1 |k summability factors.

In this paper, a known theorem dealing with | N̄, pn |k summability factors of trigonometric Fourier series has been generalized to | N̄, pn, θn |k summability. Some new results have also been obtained.

In this paper, a theorem of Bor and Özarslan [3] dealing with | C,α; β |k summability factors has been generalized for | C,α, γ ; β |k summability methods.

Revisiting the notion of μ-almost equicontinuous cellular automata introduced by R. Gilman, we show that the sequence of image measures of a shift ergodic measure μ by iterations of a μ-almost equicontinuous cellular automata F , converges in Cesaro mean to an invariant measure μc. If the initial measure μ is a Bernouilli measure, we prove that the Cesaro mean limit measure μc is shift mixing. ...

In the year 1921, Nevanlinna [7] suggested and discussed an interesting method of summation called Nq-method. Moursund [5] applied this method for summation of Fourier series and its conjugate series. Later, Moursund [6] developed Nqp-method (where p is a positive integer) and applied it to pth derived Fourier series. Samal [9] discussed Nqαmethod (0 ≤ α < 1) and studied absolute Nqα-summabilit...

We study the asymptotic behavior of random time changes dynamical systems. As we propose three classes which exhibits different patterns decays. The subordination principle may be applied to It turns out that for special case stable subordinators explicit expressions are known and its derived. For more general calculations essentially complicated reduce our corresponding Cesaro limit.

Abstract: Degree of approximation of functions of different classes has been studied by several researchers by different summability methods. In the proposed paper, we have established a new theorem for the approximation of a signal (function) belonging to the W(L r , (t))-class by (N, p n , q n )(E, s)-product summability means of a Fourier series. The result obtained here, generalizes several...