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On n -normed spaces

Author

Listed:
  • Hendra Gunawan
  • M. Mashadi

Abstract

Given an n -normed space with n ≥ 2 , we offer a simple way to derive an ( n − 1 ) -norm from the n -norm and realize that any n -normed space is an ( n − 1 ) -normed space. We also show that, in certain cases, the ( n − 1 ) -norm can be derived from the n -norm in such a way that the convergence and completeness in the n -norm is equivalent to those in the derived ( n − 1 ) -norm. Using this fact, we prove a fixed point theorem for some n -Banach spaces.

Suggested Citation

  • Hendra Gunawan & M. Mashadi, 2001. "On n -normed spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 27, pages 1-9, January.
    • Handle: RePEc:hin:jijmms:965397
    DOI: 10.1155/S0161171201010675
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