Fixed points for $k_{t+1}=\sqrt{k_t}-\frac{k_t}{2}$ For the difference equation 
$k_{t+1}=\sqrt{k_t}-\frac{k_t}{2}$
one has to find all "fixed points" and determine whether they are locally or globally asymptotically stable.
Now I'm not quite sure what "fixed point" means in this context. Is it the same as "equilibrium point" (i.e., setting $\dot{k}=0$ , and calculate $k_{t+1}=k+\dot{k}=k+0$ from there)? Or something different?
I feel confident in solving such types of DE, just not sure what "fixed point" is supposed to mean here. Thanks for providing some directions!

A fixed point in a  difference equation is similar to a fixed point in a differential equation: it is a value $k_1$ for which $k_1=k_2$.
Unfortunately, you don't have a $k_t$ on the RHS of this equation, so if you would like more specific help then you'll need to update the question.
