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.

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...