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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].