zbMATH — the first resource for mathematics

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.

40G99 Special methods of summability
42B15 Multipliers for harmonic analysis in several variables
40C05 Matrix methods for summability
Full Text: DOI
[1] Fast, H., Sur la convergence statistique, Colloq. math., 2, 241-244, (1951) · Zbl 0044.33605
[2] Freedman, A.R.; Sember, J.J.; Raphael, M., Some Cesàro type summability spaces, Proc. London math. soc., 37, 508-520, (1978) · Zbl 0424.40008
[3] Fridy, J.A.; Orhan, C., Lacunary statistical convergent, Pacific J. math., 160, 1, 43-51, (1993) · Zbl 0794.60012
[4] Hamilton, H.J., Transformations of multiple sequences, Duke math. J., 2, 29-60, (1936) · Zbl 0013.30301
[5] M. Mursaleen, O.H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl. (in press) · Zbl 1032.40001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.