A Revisit to n-Normed Spaces Through Its Quotient Spaces

H. Batkunde; H.  Gunawan

doi:10.30970/ms.53.2.181-191

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

DOI: https://doi.org/10.30970/ms.53.2.181-191

Анотація

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.

Біографія автора

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

Department of Mathematics

Посилання

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