This is a problem I figured out after seeing the definition of minimum stable point and I think the following tense is true:
Let $f(x)$ be a strictly convex function whose minimum values is $f^*=f(x^*)$. Show that $x^*$ is a stable minimum point.
Here $f:\mathbb{R}^n\rightarrow \mathbb{R}$.
Definition: A minimum point $x^*$ is said to be stable if for every minimizing sequence $f(x^k)\rightarrow f^*$ it follows that $x^k\rightarrow x^*$.
I tried to use the convexity and contradiction whit $\|x^k-x^*\|\geq \varepsilon>0$, but I can't finish it. Thanks.