Double sequence core theorems
In 1900, Pringsheim gave a definition of the convergence of double sequences. In this paper, that notion is extended by presenting definitions for the limit inferior and limit superior of double sequences. Also the core of a double sequence is defined. By using these definitions and the notion of re...
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| Format: | Article |
| Language: | English |
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Wiley
1999-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171299227858 |
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| _version_ | 1832549846662250496 |
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| author | Richard F. Patterson |
| author_facet | Richard F. Patterson |
| author_sort | Richard F. Patterson |
| collection | DOAJ |
| description | In 1900, Pringsheim gave a definition of the convergence of double sequences. In this paper, that notion is extended by presenting definitions for the limit inferior and limit superior of double sequences. Also the core of a double sequence is defined. By using these definitions and the notion of regularity for 4-dimensional matrices, extensions, and variations of the Knopp Core theorem are proved. |
| format | Article |
| id | doaj-art-3bdc7f087eb64f2b8b37b1b99c7aed7b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1999-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-3bdc7f087eb64f2b8b37b1b99c7aed7b2025-02-03T06:08:23ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251999-01-0122478579310.1155/S0161171299227858Double sequence core theoremsRichard F. Patterson0Department of Mathematics and Computer Sciences, Duquesne University, 440 College Hall, Pittsburgh 15282, PA, USAIn 1900, Pringsheim gave a definition of the convergence of double sequences. In this paper, that notion is extended by presenting definitions for the limit inferior and limit superior of double sequences. Also the core of a double sequence is defined. By using these definitions and the notion of regularity for 4-dimensional matrices, extensions, and variations of the Knopp Core theorem are proved.http://dx.doi.org/10.1155/S0161171299227858Core of a sequencedouble sequenceregular matrixP-convergent. |
| spellingShingle | Richard F. Patterson Double sequence core theorems International Journal of Mathematics and Mathematical Sciences Core of a sequence double sequence regular matrix P-convergent. |
| title | Double sequence core theorems |
| title_full | Double sequence core theorems |
| title_fullStr | Double sequence core theorems |
| title_full_unstemmed | Double sequence core theorems |
| title_short | Double sequence core theorems |
| title_sort | double sequence core theorems |
| topic | Core of a sequence double sequence regular matrix P-convergent. |
| url | http://dx.doi.org/10.1155/S0161171299227858 |
| work_keys_str_mv | AT richardfpatterson doublesequencecoretheorems |