TY - JOUR
AU - Huczek, Aleksandra
AU - WiĹ›nicki, Andrzej
PY - 2023/01/15
Y2 - 2023/02/08
TI - On the Karlssonâ€“Nussbaum conjecture for resolvents of nonexpansive mappings
JF - Annales Fennici Mathematici
JA - Ann. Fenn. Math.
VL - 48
IS - 1
SE - Articles
DO - 10.54330/afm.126009
UR - https://afm.journal.fi/article/view/126009
SP - 153-161
AB - <pre>Let \(D\subset \mathbb{R}^{n}\) be a bounded convex domain and \(F\colon D\rightarrow D\) a 1-Lipschitz mapping with respect to the Hilbert metric \(d\) on \(D\) satisfying condition \(d(sx+(1-s)y,sz+(1-s)w)\leq \max \{d(x,z),d(y,w)\}\). We show that if \(F\) does not have fixed points, then the convex hull of the accumulation points (in the norm topology) of the family \(\{R_{\lambda}\}_{\lambda >0}\) of resolvents of \(F\) is a subset of \(\partial D\). As aconsequence, we show a Wolff-Denjoy type theorem for resolvents of nonexpansive mappings acting on an ellipsoid \(D\).</pre>
ER -