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On Convergence with respect to an Ideal and a Family of Matrices
Author
Source
International Journal of Analysis
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-04-24
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
P.
Das et al.
recently introduced and studied the notions of strong AI-summability with respect to an Orlicz function F and AI-statistical convergence, where A is a nonnegative regular matrix and I is an ideal on the set of natural numbers.
In this paper, we will generalise these notions by replacing A with a family of matrices and F with a family of Orlicz functions or moduli and study the thus obtained convergence methods.
We will also give an application in Banach space theory, presenting a generalisation of Simons' sup-limsup-theorem to the newly introduced convergence methods (for the case that the filter generated by the ideal I has a countable base), continuing some of the author's previous work.
American Psychological Association (APA)
Hardtke, Jan-David. 2014. On Convergence with respect to an Ideal and a Family of Matrices. International Journal of Analysis،Vol. 2014, no. 2014, pp.1-15.
https://search.emarefa.net/detail/BIM-475818
Modern Language Association (MLA)
Hardtke, Jan-David. On Convergence with respect to an Ideal and a Family of Matrices. International Journal of Analysis No. 2014 (2014), pp.1-15.
https://search.emarefa.net/detail/BIM-475818
American Medical Association (AMA)
Hardtke, Jan-David. On Convergence with respect to an Ideal and a Family of Matrices. International Journal of Analysis. 2014. Vol. 2014, no. 2014, pp.1-15.
https://search.emarefa.net/detail/BIM-475818
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-475818