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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].