A Revisit to n-Normed Spaces Through Its Quotient Spaces

  • H. Batkunde Analysis and Geometry Research Group,Faculty of Mathematics and Natural Sciences,Bandung Institute of Technology, Bandung Indonesia
  • H. Gunawan Analysis and Geometry Research Group, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Bandung 40132, Indonesia
Keywords: continuous mappings; fixed points; n-normed spaces; quotient spaces

Abstract

In this paper, we define several types of continuous mapping in $n$-normed spaces with respect to the norms of its quotient spaces. Then, we show that all types of the continuity are equivalent. We also study contractive mappings on $n$-normed spaces using these norms. In particular, we prove a fixed point theorem for contractive mappings on a closed and bounded set in the $n$-normed space with respect to the norms of its quotient spaces.
In the last section we prove a fixed point theorem and give some remarks on the $p$-summable sequence space as an $n$-normed space.

Author Biography

H. Batkunde, Analysis and Geometry Research Group,Faculty of Mathematics and Natural Sciences,Bandung Institute of Technology, Bandung Indonesia

Department of Mathematics

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Published
2020-06-24
How to Cite
Batkunde, H., & Gunawan, H. (2020). A Revisit to n-Normed Spaces Through Its Quotient Spaces. Matematychni Studii, 53(2), 181-191. https://doi.org/10.30970/ms.53.2.181-191
Section
Articles