I-statistical Convergence of Double Sequences Defined by Weight Functions in a Locally Solid Riesz Space

Abstract

In this work, we introduce the concepts of $\mathcal{I}$-statistical convergence and $\mathcal{I}$-lacunary statistical convergence of double sequences defined by weight functions in a locally solid Riesz space based on the notion of the ideal of subsets of $\mathbb{N}\times\mathbb{N}$. We also examine some inclusion relations of these concepts.

Keywords

• Locally solid Riesz space,$\mathcal{I}$-statistical convergence,ideal convergence,double sequences

References

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