On the Karlsson–Nussbaum conjecture for resolvents of nonexpansive mappings

Authors

  • Aleksandra Huczek Pedagogical University of Krakow, Department of Mathematics
  • Andrzej Wiśnicki Pedagogical University of Krakow, Department of Mathematics

Keywords:

Karlsson–Nussbaum conjecture, Wolff–Denjoy theorem, geodesic space, Hilbert's projective metric, resolvent, nonexpansive mapping

Abstract

Let DRn be a bounded convex domain and F:DD a 1-Lipschitz mapping with respect to the Hilbert metric d on D satisfying condition d(sx+(1s)y,sz+(1s)w)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 {Rλ}λ>0 of resolvents of F is a subset of D. As aconsequence, we show a Wolff-Denjoy type theorem for resolvents of nonexpansive mappings acting on an ellipsoid D.
Section
Articles

Published

2023-01-15

How to Cite

Huczek, A., & Wiśnicki, A. (2023). On the Karlsson–Nussbaum conjecture for resolvents of nonexpansive mappings. Annales Fennici Mathematici, 48(1), 153–161. https://doi.org/10.54330/afm.126009