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

Buhyeon Kang

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.

Keywords


$\epsilon_{0}$-Cauchy sequence, $\{ \epsilon_{0}\}$-complete, $\{ \epsilon_{0}\}$-Banach spaces, generalized Banach spaces

Subject classification

03H05, 26E35

Sponsor(s)



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References


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