The σ -convergence and σ -core of a real bounded sequence were introduced in [R. Raimi, Invariant means and invariant matrix methods of summability, Duke Math. J. 30 (1963) 81–94] and [S.L. Mishra, B. Satapathy, N. Rath, Invariant means and σ -core, J. Indian Math. Soc. 60 (1984) 151–158], respectively. In this work, we extend these ideas to double sequences. c © 2006 Elsevier Ltd. All rights r...

we then write sn → s(A), where A is the A method of summability. Appropriate choices of A= [an,k] for n,k ≥ 0 give the classical methods [2]. In this paper, we present various summability analogs of the strong law of large numbers (SLLN) and their rates of convergence in an unified setting, beyond the class of random-walk methods. A convolution summability method introduced in the next section ...

In this paper we have proved some theorems on weighted mean summability method by using analytical and summability techniques, which also extends the well known result of Hardy on the Cesàro summability.

Recently, for single series, the necessary and sufficient conditions $\left\vert C,0\right\vert\Rightarrow \left\vert A_{f}\right\vert_{k}$ vise versa, A_{f}\right\vert \Rightarrow C,0\right\vert_{k}$ versa have been established, where $1 < k \infty $ $A$ is a factorable matrix. The present study extends these results to double summability, also provides some new results.

In this paper, we obtain one-sided and two-sided Tauberian conditions of Landau Hardy types for (C,1,0) (C,0,1) summability methods improper double integrals under which convergence follows from integrals. We give similar results (C,1,1) method general, in terms the concepts slowly decreasing (resp. oscillating) strong functions different senses Ces?ro real or complex-valued locally integrable ...

In this paper we present some results on convergence and summability of oneand multi-dimensional trigonometric andWalsh-Fourier series. The Fejér and Cesàro summability methods are investigated. We will prove that the maximal operator of the summability means is bounded from the corresponding classical or martingale Hardy space Hp to Lp for some p > p0. For p = 1 we obtain a weak type inequalit...