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Regular statistical convergence of double sequences

Ferenc Móricz (2005)

Colloquium Mathematicae

The concepts of statistical convergence of single and double sequences of complex numbers were introduced in [1] and [7], respectively. In this paper, we introduce the concept indicated in the title. A double sequence x j k : ( j , k ) ² is said to be regularly statistically convergent if (i) the double sequence x j k is statistically convergent to some ξ ∈ ℂ, (ii) the single sequence x j k : k is statistically convergent to some ξ j for each fixed j ∈ ℕ ∖ ₁, (iii) the single sequence x j k : j is statistically convergent to some η k for...

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