Analogues of some fundamental theorems of summability theory

Richard F. Patterson

International Journal of Mathematics and Mathematical Sciences, 2000, vol. 23, 1-9

Abstract:

In 1911, Steinhaus presented the following theorem: if A is a regular matrix then there exists a sequence of 0's and 1's which is not A -summable. In 1943, R. C. Buck characterized convergent sequences as follows: a sequence x is convergent if and only if there exists a regular matrix A which sums every subsequence of x . In this paper, definitions for subsequences of a double sequence and Pringsheim limit points of a double sequence are introduced. In addition, multidimensional analogues of Steinhaus' and Buck's theorems are proved.

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:743818

DOI: 10.1155/S0161171200001782

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