Fixed Point Theory and Applications 
Volume 2006 (2006), Article ID 78104, 15 pages
doi:10.1155/FPTA/2006/78104

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

Abstract

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.