• Korean Journal of Mathematics
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• v.27 no.3
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• pp.707-722
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• 2019

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.