Rate preservation of double sequences under l-l type transformation
Following the concepts of divergent rate preservation for ordinary sequences, we present a notion of rates preservation of divergent double sequences under l-l type transformations. Definitions for Pringsheim limit inferior and superior are also presented. These definitions and the notion of asympto...
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Hindawi Limited
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202005331 |
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doaj-f4367f80f7254adcac50a37439ff168a2020-11-24T21:46:33ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-01301063764310.1155/S0161171202005331Rate preservation of double sequences under l-l type transformationRichard F. Patterson0Department of Mathematics and Statistics, University of North Florida, Building 11, Jacksonville 32224, FL, USAFollowing the concepts of divergent rate preservation for ordinary sequences, we present a notion of rates preservation of divergent double sequences under l-l type transformations. Definitions for Pringsheim limit inferior and superior are also presented. These definitions and the notion of asymptotically equivalent double sequences, are used to present necessary and sufficient conditions on the entries of a four-dimensional matrix such that, the rate of divergence is preserved for a given double sequences under l-l type mapping where l=:{xk,l:∑k,l=1,1∞,∞|xk,l|<∞}.http://dx.doi.org/10.1155/S0161171202005331 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Richard F. Patterson |
| spellingShingle |
Richard F. Patterson Rate preservation of double sequences under l-l type transformation International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Richard F. Patterson |
| author_sort |
Richard F. Patterson |
| title |
Rate preservation of double sequences under l-l type transformation |
| title_short |
Rate preservation of double sequences under l-l type transformation |
| title_full |
Rate preservation of double sequences under l-l type transformation |
| title_fullStr |
Rate preservation of double sequences under l-l type transformation |
| title_full_unstemmed |
Rate preservation of double sequences under l-l type transformation |
| title_sort |
rate preservation of double sequences under l-l type transformation |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2002-01-01 |
| description |
Following the concepts of divergent rate preservation for ordinary sequences, we present a notion of rates preservation of divergent double sequences under l-l type transformations. Definitions for Pringsheim limit inferior and superior are also presented. These definitions and the notion of asymptotically equivalent double sequences, are used to present necessary and sufficient conditions on the entries of a four-dimensional matrix such that, the rate of divergence is preserved for a given double sequences under l-l type mapping where l=:{xk,l:∑k,l=1,1∞,∞|xk,l|<∞}. |
| url |
http://dx.doi.org/10.1155/S0161171202005331 |
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AT richardfpatterson ratepreservationofdoublesequencesunderlltypetransformation |
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