modular mappings in vector spaces over the field of complex numbers

Suppose $X$ is a $ℂ$-vector space. A mapping $\rho :X\to [0,\mathrm{\infty }]$ is called modular if the following three conditions are satisfied:

1. $\rho (x)=0$ if and only if $x=0$.

2. $\rho (\alpha x)=\rho (x)$ for all $x\in X$ and for all scalars $\alpha$ such that $|\alpha |=1$.

3. $\rho (\alpha x+\beta y)\le \rho (x)+\rho (y)$ for all $x,y\in X$ and for all scalars $\alpha$ and $\beta$ such that $\alpha +\beta =1$ and $\alpha ,\beta \ge 0$.