Notes on 2-Normed Spaces Through Their Quotient Spaces

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

Abstract


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.


Keywords


2-Banach Space, 2-normed spaces, 2-norm, quotient space

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References


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DOI: https://doi.org/10.18860/cauchy.v10i2.35824

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