New structure of norms on $\mathbb{R}^n$ and their relations with the curvature of the plane curves
Let $f_1, f_2, \ldots, f_n$ be fixed nonzero real-valued functions on $\mathbb{R}$, the real numbers. Let $\varphi_n(X_n)= \big(x_1^2f_1^2+x_2^2f_2^2+ \ldots + x_n^2f_n^2 \big)^{\frac{1}{2}}$, where $X_n=(x_1, x_2, \ldots, x_n) \in \mathbb{R}^n$. We show that $\varphi_n$ has properties similar to a...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Accademia Piceno Aprutina dei Velati
2020-12-01
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| Series: | Ratio Mathematica |
| Online Access: | http://eiris.it/ojs/index.php/ratiomathematica/article/view/552 |