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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 ϵ>0

P-lim m,n 1 mn{numbersof(j,k):j<mandk<n,|x j,k -L|ϵ}·

In this paper we introduce and study lacunary statistical convergence for double sequences and we shall also present some inclusion theorems.

40G99Special methods of summability
42B15Multipliers, several variables
40C05Matrix methods in summability