4 problems

Reflexive-space fixed point conjecture. Every reflexive Banach space has the fixed point property for nonexpansive maps. Equivalently, if $X$ is reflexive and $C\subset X$ is close…

Let $E$ be a smooth and uniformly convex Banach space of dimension two. Let $K\subseteq E$ be nonempty, closed, bounded, and convex, and let $f\colon K\to E$ be nonexpansive with…

Karlsson–Nussbaum conjecture. If $(\Sigma,\delta)$ is finite-dimensional, then there exists a convex set $\Omega\subseteq\partial\Sigma$ such that, for every $x\in\Sigma$, all accu…

Karlsson–Nussbaum conjecture. There exists a convex set $\Lambda$ in $\partial\Omega$ such that