Given a map $F:X \to X$ on a complete metric space $(X,d)$, and let $K<1$ such that:
$$ d(F(x), F(y)) \le K d(x,y), \quad \forall x,y \in X $$
then the contraction mapping theorem tells us that $F$ has a unique fixed point, and we can iteratively solve for this fixed point.
My question is, if we take $K=1$, then it is no longer a contraction, I've seen this being called a 'non-strict' contraction. I'm wondering if there are any results regarding this case and fixed points? Do they exist but aren't unique, or do they not exist at all?