Fixed Point Theory and Applications
Volume 2006 (2006), Article ID 78104, 15 pages

Hyperbolic monotonicity in the Hilbert ball

Eva Kopecká1,2 and Simeon Reich3

1Institute of Mathematics, Czech Academy of Sciences, Žitná 25, Prague 11567, Czech Republic
2Institut für Analysis, Johannes Kepler Universität, Linz 4040, Austria
3Department of Mathematics, The Technion – Israel Institute of Technology, Haifa 32000, Israel

Received 17 August 2005; Accepted 22 August 2005

Copyright © 2006 Eva Kopecká and Simeon Reich. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We first characterize ρ-monotone mappings on the Hilbert ball by using their resolvents and then study the asymptotic behavior of compositions and convex combinations of these resolvents.