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Journals / Gazi University Journal of Science Part A: Engineering and Innovation / 2026 / Volume: 10 Issue: 1

Hilbert I-Statistical Convergence on Neutrosophic Normed Spaces

Nazmiye Gönül Bilgin(Zonguldak Bülent Ecevit Üniversitesi)0000-0001-6300-6889
Pages
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Publication Date
2023-03-28
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

As a result, it is thought that the selected convergence type is suitable for the Neutrosophic normed space structure and is a guide for new convergence types.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, λI-statistical convergence is defined to generalize statistical convergence on Neutrosophic normed spaces.
📊
Key Findings & Data:As it is known, Neutrosophic theory, which brings a new breath to daily life and complex scientific studies which we encounter with many uncertainties, is a rapidly developing field with many new study subjects.
💡
Conclusion & Impact:As a result, it is thought that the selected convergence type is suitable for the Neutrosophic normed space structure and is a guide for new convergence types.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Neutrosophic Normed Spaces · Hilbert Matrix · Statistical Convergence

Abstract

In this paper, λI-statistical convergence is defined to generalize statistical convergence on Neutrosophic normed spaces. As it is known, Neutrosophic theory, which brings a new breath to daily life and complex scientific studies which we encounter with many uncertainties, is a rapidly developing field with many new study subjects. Thus, researchers show great interest in this philosophical approach and try to transfer related topics to this field quickly. For this purpose, in this study, besides the definition of λI-statistical convergence, the important features of Hilbert sequence space and λI-statistical convergence in Neutrosophic spaces are examined with the help of these defined sequences. By giving the relationship between Hilbert λI-statistical convergence and Hilbert I-statistical convergence, it has been evaluated whether the definitions contain a coverage relationship as in fuzzy and intuitionistic fuzzy. As a result, it is thought that the selected convergence type is suitable for the Neutrosophic normed space structure and is a guide for new convergence types.

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Cite This Article

Bilgin, N. G. (2023). Hilbert I-Statistical Convergence on Neutrosophic Normed Spaces. Gazi University Journal of Science Part A: Engineering and Innovation, Volume: 10 Issue: 1. https://doi.org/10.54287/gujsa.1168439

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