Korean J. Math. Vol. 27 No. 3 (2019) pp.707-722
DOI: https://doi.org/10.11568/kjm.2019.27.3.707

On the generalized Banach spaces

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Published: Sep 30, 2019
Keywords:
$\epsilon_{0}$-Cauchy sequence, $\{ \epsilon_{0}\}$-complete, $\{ \epsilon_{0}\}$-Banach spaces, generalized Banach spaces
Mathematics Subject Classification:
03H05, 26E35

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Buhyeon Kang
Department of Mathematics Seokyeong University Seoul 02713, Korea

Abstract

For any non-negative real number $\epsilon_{0}$, we shall introduce a concept of the $\epsilon_{0}$-Cauchy sequence in a normed linear space $V$ and also introduce a concept of the $\epsilon_{0}$-completeness in those spaces. Finally we introduce a concept of the generalized Banach spaces with these concepts.


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