11.1 Find all functions \( f: \mathbb{R} \rightarrow \mathbb{R} \), which for all \( x \), \( y \), \( z \in \mathbb{R} \) satisfy the inequality
\[
\begin{array}{l}
f(x+\dot{y})+f(y+z)+f(z+x) \\
\geqslant 3 f(x+2 y+3 z) .
\end{array}
\]
11.1 Let $x=y=-2$, we get $f(2 x)+j(0)+$ $f(0) \geqslant 3 f(0)$, thus $f(2 x) \geqslant f(0)$.

On the other hand, let $x=z=-y$, we get $f(0)+f(0)+$ $f(2 x) \geqslant 3 f(2 x)$, hence $f(2 x) \leqslant f(0)$. Therefore, $f(0)$ $\geqslant f(2 x) \geqslant f(0)$. That is, $f(2 x) \equiv$ constant $=c$. It is easy to verify that for any $c \in \mathbb{R}$, the function $f(x) \equiv c$ satisfies the condition.