  Given a smooth, symmetric, homogeneous of degree one function
$f\left(\lambda_{1},\cdots,\,\lambda_{n}\right)$ satisfying $\partial_{i}f>0$
for all $i=1,\cdots,\,n$, and a rotationally symmetric cone $\mathcal{C}$ in
$\mathbb{R}^{n+1}$, we show that there is a $f$ self-shrinker (i.e. a
hypersurface $\Sigma$ in $\mathbb{R}^{n+1}$ which satisfies
$f\left(\kappa_{1},\cdots,\,\kappa_{n}\right)+\frac{1}{2}X\cdot N=0$, where $X$
is the position vector, $N$ is the unit normal vector, and
$\kappa_{1},\cdots,\,\kappa_{n}$ are principal curvatures of $\Sigma$) that is
asymptotic to $\mathcal{C}$ at infinity.
