A revisit to n-normed spaces through its quotient spaces
Batkunde H.a, Gunawan H.a
a Analysis and Geometry Research Group, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Bandung, Indonesia
Abstract
© H. Batkunde, H. Gunawan, 2020.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 keywords
Indexed keywords
Continuous mappings,Fixed points,N-normed spaces,Quotient spaces.
Funding details
Acknowledgments. This work is supported by ITB Research and Innovation Program 2019. The first author is also supported by LPDP Indonesia.