Attainment of the minimal displacement for non-expansive operators in Hilbert spaces
Applicable Nonlinear Analysis, Volume 2, Issue 2, August 2025, Pages: 91–96
BIAGIO RICCERI
Department of Mathematics and Informatics, University of Catania, Viale A. Doria 95125 Catania, Italy
Abstract
Let \(H\) be a real Hilbert space and let \(T:H\to H\) be a sequentially weakly continuous operator which is non-expansive with respect to some norm on \(H\) equivalent to \(\|\cdot\|_H\). In this paper, we provide a sufficient condition ensuring the existence of a point \(\tilde x\in H\) such that \[\|\tilde x-T(\tilde x)\|_H=\inf_{x\in H}\|x-T(x)\|_H.\]
Cite this Article as
Biagio Ricceri, Attainment of the minimal displacement for non-expansive operators in Hilbert spaces, Applicable Nonlinear Analysis, 2(2), 91–96, 2025