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


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.


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

Subject classification

03H05, 26E35


Full Text:



Chawalit Boonpok, Generalized (Λ,b)-closed sets in topological spaces, Korean J. Math. 25 (3) (2017). (Google Scholar)

Hi-joon Chae, Byungheup Jun, and Jungyun Lee, Continued fractions and the density of graphs of some functions, Korean J. Math. 25 (2) (2017). (Google Scholar)

D. L. Cohn, Measure Theory, Berkhauser Boston. (1980). (Google Scholar)

B. H. Kang, An Introduction to ε0−Density and ε0−Dense Ace, JCMS vol31. (2018) (Google Scholar)

B. H. Kang, The sequential attainability and attainable ace, Korean J. Math. 26 (4) (2018). (Google Scholar)

E. Hewitt, K. Stromberg, Real and Abstract Analysis, Springer-Verlag (1965). (Google Scholar)


  • There are currently no refbacks.

ISSN: 1976-8605 (Print), 2288-1433 (Online)

Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: kkms@kangwon.ac.kr