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

Year 2019, Volume: 7 Issue: 1, 55 - 61, 15.04.2019

Şükran Konca , Ergin Genç Mehmet Küçükaslan

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

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