Fridy and Miller have given a characterization of statistical convergence for bounded single sequence, by matrix summability methods. The analogues of the some of the results for double sequences were proved by H.I. Miller and Leila Miller-Van Wieren. In this paper we define the statistical convergence of double sequences in a non-trivially valued non-archimedean field K and prove a theorem on ...

Abstract The general entire solution to a linear system of moment differential equations is obtained in terms kernel function for generalized summability, and the Jordan decomposition matrix defining problem. growth at infinity any also determined, both globally following rays infinity, determining order type such solutions.

We consider the summability of oneand multi-dimensional trigonometric Fourier series. The Fejér and Riesz summability methods are investigated in detail. Different types of summation and convergence are considered. We will prove that the maximal operator of the summability means is bounded from the Hardy space Hp to Lp, for all p > p0, where p0 depends on the summability method and the dimensio...

determined by the matrix A =(a„fc) of real or complex constants, if the transform S» exists and limn^S„ = L. The matrix A (and method of summability A) is called row-finite if for each n, a„k = 0 for all sufficiently great k; and is called triangular if an* = 0 for k>n. The method A is regular if sn—>L implies Sn-*L. Necessary and sufficient conditions that A be regular are, by the Silverman-To...

We prove the necessary and sufficient conditions for an infinity matrix to be a mapping, from absolutely convergent series to convergent sequences, which is treated as general weighted mean summability methods. The results include a classical result by Hardy and another by Moricz and Rhoades as particular cases.

The purpose of this paper is to investigate the effects of fourdimensional summability matrix methods on the A-statistical approximation of sequences of positive linear operators defined on the space of all real valued Bögel-type continuous functions on a compact subset of the real line. Furthermore, we study the rates of A-statistical convergence in our approximation. Mathematics Subject Class...

Let $(u_n)$ be a sequence of fuzzy numbers.  We recover the slow oscillation of $(u_n)$ of fuzzy numbers from the Ces`{a}ro summability of its generator sequence and some additional conditions imposed on $(u_n)$. Further, fuzzy analogues of some well known classical Tauberian theorems for Ces`{a}ro summability method are established as particular cases.

In this paper, following the methods of Connor, we introduce some new generalized double difference sequence spaces using summability with respect to a two valued measure, double infinite matrix and an Orlicz function in 2normed spaces which have unique non-linear structure and examine some of their properties.