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Journals / Gazi University Journal of Science / 2016 / Cilt: 29 - Sayı: 4

ON THE EQUIVALENCE OF CONVERGENCE AND 2-NORM CONVERGENCE IN NORMED SPACES

Bahri TURAN
Fatma BİLİCİ
Pages
879–881
Publication Date
2016-12-19
DOI
—
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AI Summary & Key Takeaways

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

In this paper, we show that ∥.∥-convergence and ∥.,.∥_{G}2-convergence are equivalent.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Let (X,∥.∥) be a normed space and ∥.,...,.∥_{G} be the n-norm given by Gähler.
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Key Findings & Data:Let (X,∥.∥) be a normed space and ∥.,...,.∥_{G} be the n-norm given by Gähler.
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Conclusion & Impact:In this paper, we show that ∥.∥-convergence and ∥.,.∥_{G}2-convergence are equivalent.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Normed space · n-normed space · n-Banach space

Abstract

Let (X,∥.∥) be a normed space and ∥.,...,.∥_{G} be the n-norm given by Gähler. In this paper, we show that ∥.∥-convergence and ∥.,.∥_{G}2-convergence are equivalent.

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Cite This Article

TURAN, B., BİLİCİ, F. (2016). ON THE EQUIVALENCE OF CONVERGENCE AND 2-NORM CONVERGENCE IN NORMED SPACES. Gazi University Journal of Science, Cilt: 29 - Sayı: 4, 879–881. https://ajindex.com/articles/254582

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References (5)

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  2. Gunawan, H., The space of p-summable sequences and its natural n-norms, Bull. Austral. Math. Soc. 64, 137--147, (2001).
  3. Gunawan, H. and Mashadi, M., On n-normed spaces, Int. J. Math. Math. Sci. 27, 631--639, (2001).
  4. Raymond, W. and Freese, Yeol Je Cho, Geometry of linear 2-normed spaces, Nova Science publishers, Inc, Newyork, (2001).
  5. Turan, B. and Bilici, F., On almost 2-normed vector lattice, Preprint. White, A., 2-Banach Spaces, Doctoral Dissertation, Saint Louis University, (1968).