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The concept of n-bounded and n-continuous operators is discussed as an extension of the concept introduced in [12]. The equivalence of three statements on n-continuity and n-boundedness of a linear operator from a normed space into an n-normed space is also proved. This newly introduced concept is proved to be identical to one type of n-continuity introduced in [12].


n-normed space n-bounded operator n-continuous operator

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How to Cite
Soibam, R. M. (2022). n-Boundedness and n-Continuity of Linear Operators. Journal of the Indonesian Mathematical Society, 28(2), 147–157.


  1. Diminnie, C., G¨ahler, S. and White, A., “2-inner product spaces”, Demonstratio Math. 6(1973), 525 − 536.
  2. G¨ahler, S., “Lineare 2-normerte r¨aume”, Math. Nachr. 28 (1964), 1-43.
  3. G¨ahler, S., “Untersuchungen ¨uber verallgemeinerte m-metrische r¨aume I”, Math. Nachr. 40(1969), 165-189.
  4. G¨ahler, S., “Untersuchungen ¨uber verallgemeinerte m-metrische r¨aume II”, Math. Nachr. 40(1969),229-264.
  5. G¨ahler, S. , “Untersuchungen ¨uber verallgemeinerte m-metrische r¨aume III”, Math. Nachr. 41(1970), 23-36
  6. Gozali, S. M. , Gunawan, H. and Neswan, O., “On n-norms and bounded n-linear functionals in a Hilbert space” Ann. Funct. Anal. 1 (2010), 72-79.
  7. Gunawan, H. and Mashadi, “On n-normed spaces” Int. J. Math. Math. Sci. 27 (2001), 631-639.
  8. Gunawan, H., “The space of p-summable sequences and its natural n-norms” Bull. Austral. Math. Soc. 64 (2001), 137-147.
  9. Lewandowska, Z., “Bounded 2-linear operators on 2-normed sets” Glasnik MateMaticki 39 (2004), 303-314.
  10. Misiak, A., “n-inner product spaces.” Math. Nachr. 140 (1989) 299-319.
  11. Pangalela, Y. E. P. and Gunawan, H., “The n-dual space of p-summabe sequences” Mathematica Bohemica 138(2013), 439-448.
  12. Soenjaya, A. L., “On n-bounded and n-continuous operator in n-normed space” J. Indones. Math. Soc. 18(2012), 45-56.
  13. White, A., “2-Banach spaces.” Math. Nachr. 42 (1969), 43-60