On n-normed spaces
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201010675 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |