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}
}
  • B. Ricceri
  • Published 22 July 2020
  • Mathematics
  • arXiv: Functional Analysis
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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Italy e-mail address: ricceri@dmi