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Let $E$ be a Banach space, $T:E\rightarrow E$ a continuous bounded nonlinear mapping., and $\{x_n\}_{n\in\mathbb N}$ such that $$x_{n+1}=T(x_n),\:\forall n\in \mathbb{N}:=\{0,1,\cdots\}.$$ Let $$X_n=\...

Call trajectory any continuous function $f: \mathbb{R}_{\geq 0} \to \mathbb{R}^n$ (here, $\mathbb{R}_{\geq 0}$ is interpreted as time). A polyhedral partition of $\mathbb{R}^n$ is a finite set of ...

This is a weak version of this problem, written down in Lviv Scottish Book. I start with necessary definitions. Let $K=-K$ be a centrally symmetric compact convex body in the Euclidean space $\mathbb ...