Notes on 2-Normed Spaces Through Their Quotient Spaces

Rumlawang, Francis Yunito
Hernita, Hernita
Lesnussa, Yopi Andry
Batkunde, Harmanus

CAUCHY: Jurnal Matematika Murni dan Aplikasi
Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI

In this paper, we defined new norms in 2-normed spaces derived from the 2-norm with respect to its quotient spaces. Moreover, these norms were used to observe some aspects of 2-normed spaces namely, a Convergent sequence, a Cauchy sequence, completeness, a closed set, and a bounded set. Furthermore, we used these aspects to prove the Fixed-Point Theorem in a 2-Banach Space.