An Invitation to the Study of a Uniqueness Problem

@article{Ricceri2020AnIT,
title={An Invitation to the Study of a Uniqueness Problem},
author={Biagio Ricceri},
journal={arXiv: Functional Analysis},
year={2020}
}

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 $X$.

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