I-WEIGHTED LACUNARY STATISTICAL tau-CONVERGENCE IN LOCALLY SOLID RIESZ SPACES

Abstract

An ideal $I$ is a family of positive integers $\mathbb{N}$ which is closed under taking finite unions and subsets of its elements. In this  paper, we introduce the notions of ideal versions of weighted lacunary statistical $\tau$-convergence, statistical $\tau$-Cauchy, weighted lacunary $\tau$-boundedness of sequences in locally solid Riesz spaces endowed with the topology $\tau$. We also prove some topological results related to these concepts in locally solid Riesz space.

Keywords

• Ordered topological vector space; locally solid Riesz space; $I$-weighted lacunary statistical $\tau$-convergence; I-convergence

References

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