Ideal convergence generated by double summability methods
Abstract: The main result of this note is that if I is an ideal generated by a regular double summability matrix summability method T that is the product of two nonnegative regular matrix methods for single sequences, then I-statistical convergence and convergence in I-density are equivalent. In particular, the method T generates a density µT with the additive property (AP) and hence, the additive property for null sets (APO). The densities used to generate statistical convergence, lacunary statistical convergence, and general de la Vallée-Poussin statistical convergence are generated by these types of double summability methods. If a matrix T generates a density with the additive property then T-statistical convergence, convergence in T-density and strong T-summabilty are equivalent for bounded sequences. An example is given to show that not every regular double summability matrix generates a density with additve property for null sets.
- Standort
-
Deutsche Nationalbibliothek Frankfurt am Main
- Umfang
-
Online-Ressource
- Sprache
-
Englisch
- Erschienen in
-
Ideal convergence generated by double summability methods ; volume:49 ; number:1 ; year:2016 ; pages:26-37 ; extent:12
Demonstratio mathematica ; 49, Heft 1 (2016), 26-37 (gesamt 12)
- Urheber
-
Connor, Jeff
- DOI
-
10.1515/dema-2016-0004
- URN
-
urn:nbn:de:101:1-2411181447090.020697241502
- Rechteinformation
-
Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Letzte Aktualisierung
-
15.08.2025, 07:22 MESZ
Datenpartner
Deutsche Nationalbibliothek. Bei Fragen zum Objekt wenden Sie sich bitte an den Datenpartner.
Beteiligte
- Connor, Jeff
Ähnliche Objekte (12)
Regularly ideal invariant convergence of double sequences
On some results in intuitionistic fuzzy ideal convergence double sequence spaces
Convergence of measures on minimally generated boolean algebras
On Some New Sequence Spaces and Statistical Convergence Methods for Double Sequences
An operator ideal generated by Orlicz spaces
Boolean Algebras Whose Ideals Are Disjointly Generated
Some new lacunary statistical convergence with ideals
On ideal convergence Fibonacci difference sequence spaces
Computational Ideal Theory in Finitely Generated Extension Rings
Local convergence of tensor methods
CONVERGENCE WITH RESPECT TO THE MYCIELSKI ɑ-IDEAL
On statistical convergence and strong Cesàro convergence by moduli for double sequences
Regularly ideal invariant convergence of double sequences
On some results in intuitionistic fuzzy ideal convergence double sequence spaces
Convergence of measures on minimally generated boolean algebras
On Some New Sequence Spaces and Statistical Convergence Methods for Double Sequences
An operator ideal generated by Orlicz spaces
Boolean Algebras Whose Ideals Are Disjointly Generated
Some new lacunary statistical convergence with ideals
On ideal convergence Fibonacci difference sequence spaces
Computational Ideal Theory in Finitely Generated Extension Rings
Local convergence of tensor methods
CONVERGENCE WITH RESPECT TO THE MYCIELSKI ɑ-IDEAL
On statistical convergence and strong Cesàro convergence by moduli for double sequences
Regularly ideal invariant convergence of double sequences
On some results in intuitionistic fuzzy ideal convergence double sequence spaces
Convergence of measures on minimally generated boolean algebras
On Some New Sequence Spaces and Statistical Convergence Methods for Double Sequences
An operator ideal generated by Orlicz spaces
Boolean Algebras Whose Ideals Are Disjointly Generated
Some new lacunary statistical convergence with ideals
On ideal convergence Fibonacci difference sequence spaces
Computational Ideal Theory in Finitely Generated Extension Rings
Local convergence of tensor methods
CONVERGENCE WITH RESPECT TO THE MYCIELSKI ɑ-IDEAL