Statistical Order Convergence and Statistically Relatively Uniform Convergence in Riesz Spaces
A new concept of statistically e-uniform Cauchy sequences is introduced to study statistical order convergence, statistically relatively uniform convergence, and norm statistical convergence in Riesz spaces. We prove that, for statistically e-uniform Cauchy sequences, these three kinds of convergenc...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/9092136 |
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| _version_ | 1832565123377528832 |
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| author | Xuemei Xue Jian Tao |
| author_facet | Xuemei Xue Jian Tao |
| author_sort | Xuemei Xue |
| collection | DOAJ |
| description | A new concept of statistically e-uniform Cauchy sequences is introduced to study statistical order convergence, statistically relatively uniform convergence, and norm statistical convergence in Riesz spaces. We prove that, for statistically e-uniform Cauchy sequences, these three kinds of convergence for sequences coincide. Moreover, we show that the statistical order convergence and the statistically relatively uniform convergence need not be equivalent. Finally, we prove that, for monotone sequences in Banach lattices, the norm statistical convergence coincides with the weak statistical convergence. |
| format | Article |
| id | doaj-art-b387165828144909a0cb0f190b458410 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-b387165828144909a0cb0f190b4584102025-02-03T01:09:29ZengWileyJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/90921369092136Statistical Order Convergence and Statistically Relatively Uniform Convergence in Riesz SpacesXuemei Xue0Jian Tao1School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, ChinaSchool of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, ChinaA new concept of statistically e-uniform Cauchy sequences is introduced to study statistical order convergence, statistically relatively uniform convergence, and norm statistical convergence in Riesz spaces. We prove that, for statistically e-uniform Cauchy sequences, these three kinds of convergence for sequences coincide. Moreover, we show that the statistical order convergence and the statistically relatively uniform convergence need not be equivalent. Finally, we prove that, for monotone sequences in Banach lattices, the norm statistical convergence coincides with the weak statistical convergence.http://dx.doi.org/10.1155/2018/9092136 |
| spellingShingle | Xuemei Xue Jian Tao Statistical Order Convergence and Statistically Relatively Uniform Convergence in Riesz Spaces Journal of Function Spaces |
| title | Statistical Order Convergence and Statistically Relatively Uniform Convergence in Riesz Spaces |
| title_full | Statistical Order Convergence and Statistically Relatively Uniform Convergence in Riesz Spaces |
| title_fullStr | Statistical Order Convergence and Statistically Relatively Uniform Convergence in Riesz Spaces |
| title_full_unstemmed | Statistical Order Convergence and Statistically Relatively Uniform Convergence in Riesz Spaces |
| title_short | Statistical Order Convergence and Statistically Relatively Uniform Convergence in Riesz Spaces |
| title_sort | statistical order convergence and statistically relatively uniform convergence in riesz spaces |
| url | http://dx.doi.org/10.1155/2018/9092136 |
| work_keys_str_mv | AT xuemeixue statisticalorderconvergenceandstatisticallyrelativelyuniformconvergenceinrieszspaces AT jiantao statisticalorderconvergenceandstatisticallyrelativelyuniformconvergenceinrieszspaces |