Analogues of some fundamental theorems of summability theory
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 whi...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171200001782 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |