An invitation to the study of a uniqueness problem

Abstract

In this very short paper, we provide a strong motivation for the study of the following problem: given a real normed space $E$, a closed, convex, unbounded set $X\subseteq E$ and a function $f:X\to X$, find suitable conditions under which, for each $y\in X$, the function $$x\to \|x-f(x)\|-\|y-f(x)\|$$ has at most one global minimum in $X$.