Statistical Order Convergence and Statistically Relatively Uniform Convergence in Riesz Spaces
Joint Authors
Source
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-04-15
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Xue, Xuemei& Tao, Jian. 2018. Statistical Order Convergence and Statistically Relatively Uniform Convergence in Riesz Spaces. Journal of Function Spaces،Vol. 2018, no. 2018, pp.1-9.
https://search.emarefa.net/detail/BIM-1186706
Modern Language Association (MLA)
Xue, Xuemei& Tao, Jian. Statistical Order Convergence and Statistically Relatively Uniform Convergence in Riesz Spaces. Journal of Function Spaces No. 2018 (2018), pp.1-9.
https://search.emarefa.net/detail/BIM-1186706
American Medical Association (AMA)
Xue, Xuemei& Tao, Jian. Statistical Order Convergence and Statistically Relatively Uniform Convergence in Riesz Spaces. Journal of Function Spaces. 2018. Vol. 2018, no. 2018, pp.1-9.
https://search.emarefa.net/detail/BIM-1186706
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1186706