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Dergiler / 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
Sayfa
879–881
Yayın Tarihi
2016-12-19
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Let (X,∥.∥) be a normed space and ∥.,...,.∥_{G} be the n-norm given by Gähler.
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Temel Bulgular & Veri:Let (X,∥.∥) be a normed space and ∥.,...,.∥_{G} be the n-norm given by Gähler.
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Sonuç & Katkı:In this paper, we show that ∥.∥-convergence and ∥.,.∥_{G}2-convergence are equivalent.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

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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Kaynakça (5)

  1. Gähler, S., Lineare 2-normierte räume, Math. Nachr. 28, 1-43, (1964). Gähler, S., Untersuchungen ¨uber verallgemeinerte m-metrische R¨aume. I, Math. Nachr., 40, 165--189, (1969).
  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).