Abstract
In this paper, we introduce and study the notion of rough mathcal {I}_{2}-lacunary statistical convergence of double sequences in normed linear spaces. We also introduce the notion of rough mathcal{I}_{2}-lacunary statistical limit set of a double sequence and discuss some properties of this set.
Highlights
Throughout the paper, N and R denote the set of all positive integers and the set of all real numbers, respectively
The idea of I-convergence was introduced by Kostyrko et al [6] as a generalization of statistical convergence which is based on the structure of the ideal I of subset of the set of natural numbers
A lot of development have been made in area about statistical convergence, I-convergence and double sequences after the work of [1, 2, 10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28]
Summary
Throughout the paper, N and R denote the set of all positive integers and the set of all real numbers, respectively. A double sequence x = {xjk} of real numbers is I2-statistically convergent to ε, and we write x I→2-st ξ , provided that for any ε > 0 and δ > 0 (m, n) ∈ N × N: 1 mn (j, k) : xjk – ξ ≥ ε, j ≤ m, k ≤ n A double sequence x = {xmn} of numbers is said to be I2-lacunary statistical convergent or Sθ2 (I2)-convergent to L, if for each ε > 0 and δ > 0, (u, s) ∈ N × N : 1 hus (m, n) ∈ Jus : |xmn – L| ≥ ε
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