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On acceleration convergence of multiple sequences

Hazarika B

Fasciculi Mathematici

2013

Nr 51

85--92

In this article the notion of acceleration convergence of double sequences in Pringsheim’s sense has been introduced and some theorems related to that concept have been established using the four dimensional matrix transformations.

On asymptotically statistical equivalent sequences

Patterson R. F.

Demonstratio Mathematica

2003

Vol. 36, nr 1

149--153

This paper presents the following definition which is a natural combination of the definition for Asymptotically equivalent and Statistically limit. Two nonnegative sequences [x] and [y] are said to be asymptotically statistical equivalents of multiple L provided that for every e > 0, limn 1/n{the number of k < n : |xk/yk-L\ > e} = 0 (denoted by x Sl y), and simply asymptotically statistical equivalent if L = 1. In addition, there are also statistical analogs of theorems of Poyvanents in [5].

Characterization for the limit points of stretched double sequences

Patterson R. F.

Demonstratio Mathematica

2002

Vol. 35, nr 1

103-109

This paper investigates the effect of four dimensional matrix transformation on new classes of double sequences. Subsequences and stretchings of a double sequence are denned, and these definitions are used to present a four dimensional analogue of D. Dawson's Copy theorem for stretchings of a double sequence. In addition, the multidimensional analogue of D. Dawson's Copy theorem is used to characterize convergent double sequences using subsequences and stretchings.

A characterization for the limit points of double sequences

Patterson R.

Demonstratio Mathematica

1999

Vol. 32, nr 4

775-780

In 1944 R.P Agnew characterized limit points of single dimensional sequences by provIng the following: Let A be regular and let xn be a bounded complex sequence, then there exIsts a subsequence yn of xn such that the set Ly of limit points of the transform Yn of yn includes the set Lx of limit points of the sequence xn . In this paper we shall use the definition of Pringsheim limit points in [6] to present a multidimensional analogues of Agnew result in [1].