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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
We also prove some topological results related to these concepts in locally solid Riesz space.
📌 3 Key Takeaways
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Objective & Hypothesis:An ideal $I$ is a family of positive integers $\mathbb{N}$ which is closed under taking finite unions and subsets of its elements.
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Key Findings & Data: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 $\tau$.
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Conclusion & Impact:We also prove some topological results related to these concepts in locally solid Riesz space.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Ordered topological vector space · locally solid Riesz space · $I$-weighted lacunary statistical $\tau$-convergence
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.
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Cite This Article
KONCA, Ş., GENÇ, E. (2019). I-WEIGHTED LACUNARY STATISTICAL tau-CONVERGENCE IN LOCALLY SOLID RIESZ SPACES. Journal of Universal Mathematics, Cilt: 2 - Sayı: 1, 22–31. https://ajindex.com/articles/782225