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 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 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 investigate some Tauberian conditions in terms of the general control modulo of the oscillatory behavior of integer order of continuous real functions on [0,∞) for (C, 1) summability of integrals. Moreover, we obtain a Tauberian theorem for a real bounded function on [0,∞).

It is proved that the maximal operator of the l1-Fejér means of a d-dimensional Fourier series is bounded from the periodic Hardy space Hp(T ) to L p(T ) for all d/(d+1) < p ≤ ∞ and, consequently, is of weak type (1, 1). As a consequence we obtain that the l1-Fejér means of a function f ∈ L1(T ) converge a.e. to f . Moreover, we prove that the l1-Fejér means are uniformly bounded on the spaces ...

In this paper, we prove a general theorem dealing with |C,α ,γ ,β ;σ |k summability factors by using a general class of power increasing sequences instead of an almost increasing sequence. This theorem also includes several known and new results.

In this paper we obtain some sufficient conditions on |N, pn, qn|k summability of an orthogonal series. These conditions are expressed in terms of the coefficients of the orthogonal series. Also, several known and new results are deduced as corollaries of the main results. c ©2014 All rights reserved.

Statistical convergence for sequences of fuzzy real numbers has been studied by various authors. In this paper we study the concept of statistical summability (C, 1) for fuzzy real numbers which for real numbers was introduced by Moricz [18]. We also construct some interesting examples. AMS Mathematical Subject Classification: 40A30, 40E05, 94D05