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Lacunary statistical convergence of multiple sequences. (English) Zbl 1132.40312
Summary: Quite recently, Mursaleen and O. H. H. Edely [J. Math. Anal. Appl. 288, No. 1, 223–231 (2003; Zbl 1032.40001)], defined the statistical analogue for double sequences \(x=\{x_{k,l}\}\) as follows: A real double sequence \(x=\{x_{k,l}\}\) is said to be P-statistically convergent to \(L\) provided that for each \(\epsilon >0\)
\[ P-\lim_{m,n} \frac{1}{mn}\{\text{ numbers of } (j,k):j<m \text{ and } k<n, |x_{j,k}-L|\geq\epsilon\}. \]
In this paper we introduce and study lacunary statistical convergence for double sequences and we shall also present some inclusion theorems.

MSC:
40G99 Special methods of summability
42B15 Multipliers for harmonic analysis in several variables
40C05 Matrix methods for summability
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