Double lacunary density and lacunary statistical convergence of double sequences. (English) Zbl 1240.40021

Çakan, Celal; Altay, Bilal; Çoşkun, Hüsamettin

Stud. Sci. Math. Hung. 47, No. 1, 35-45 (2010).

Using Pringsheim’s notion of convergence for double sequences, the authors introduce the double lacunary density of subsets of \(\mathbb{N}\times \mathbb{N}\) and study relations between this new density and lacunary statistical convergence of double sequences. There are some misprints and errors in the authors’ presentation.

Reviewer: Toivo Leiger (Tartu)

MSC:

40C05	Matrix methods for summability
40J05	Summability in abstract structures (should also be assigned at least one other classification number from Section 40-XX)
46A45	Sequence spaces (including Köthe sequence spaces)
40B05	Multiple sequences and series (should also be assigned at least one other classification number in this section)
40A35	Ideal and statistical convergence

Keywords:

double sequences; four dimensional matrices; core theorems and matrix transformations; Pringsheim convergence