On Convergence with respect to an Ideal and a Family of Matrices

Jan-David Hardtke

International Journal of Analysis, 2014, vol. 2014, 1-15

Abstract:

P. Das et al. recently introduced and studied the notions of strong -summability with respect to an Orlicz function and -statistical convergence, where is a nonnegative regular matrix and is an ideal on the set of natural numbers. In this paper, we will generalise these notions by replacing with a family of matrices and 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 has a countable base), continuing some of the author's previous work.

Date: 2014
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/ANALYSIS/2014/490904.pdf (application/pdf)
http://downloads.hindawi.com/journals/ANALYSIS/2014/490904.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:ijanal:490904

DOI: 10.1155/2014/490904

Access Statistics for this article

More articles in International Journal of Analysis from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().