On the structure of fixed-point sets of asymptotically regular mappings in Hilbert spaces
Let \(H\) be a Hilbert space, \(C\in X\) a nonempty bounded closed convex set, \(T: C\to C\) such that, for every \(x\in X\), \(\lim|T^n(x), T^{n+1}(x)|= 0\) and \(\liminf\| T^n(x)\|< \sqrt{2}\) if \(n\to\infty\). By using techniques of asymptotic center, the author gives an elementary proof of the existence of fixed points of \(T\) and proves that the set of fixed points of \(T\) is a retract of \(C\).
scientific article; zbMATH DE number 5734962