The representation of \(n\)-collinearity in \(n\)-normed space. (English) Zbl 1486.46010
Summary: In a \(n\)-normed space \(X\), for the \(n\)-collinear elements \(u,x_1,\ldots,x_n\), we prove the uniqueness of \(u\) such that \(u,x_1,\ldots,x_n\) satisfy some inequalities. This answers two open questions given by W. Shatanawi and M. Postolache [Nonlinear Sci. Appl. 9, No. 5, 3066–3073 (2016; Zbl 1358.46021)].
MSC:
| 46B04 | Isometric theory of Banach spaces |
| 46B20 | Geometry and structure of normed linear spaces |
| 51K05 | General theory of distance geometry |
