Some new double sequence spaces of invariant means. (English) Zbl 1195.46005

Mursaleen, M.; Mohiuddine, S. A.

Glas. Mat., III. Ser. 45, No. 1, 139-153 (2010).

Summary: We define some new spaces of double sequences involving the idea of \(\sigma \)-mean; i.e., we define the spaces of strongly \(\sigma \)-convergent, absolutely \(\sigma \)-almost convergent, \(\sigma \)-almost bounded and absolutely \(\sigma \)-convergent double sequences and establish some inclusion relations along with some numerical examples.

MSC:

46A45	Sequence spaces (including Köthe sequence spaces)
40C05	Matrix methods for summability
40H05	Functional analytic methods in summability

Keywords:

double sequences; absolute almost convergence; \(\sigma \)-mean; strong \(\sigma \)-convergence; absolute \(\sigma \)-convergence; \(\sigma \)-almost boundedness; absolute \(\sigma \)-convergence