 CARMA ANALYSIS AND NUMBER THEORY SEMINAR
 Speaker: Mr David ArizaRuiz, Department of Mathematical Analysis, University of Seville
 Title: On firmly nonexpansive mappings with an introduction to geodesic metric spaces
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 1:00 pm, Tue, 6^{th} Mar 2012
 Abstract:
We start this talk by introducing some basic definitions and properties relative to geodesic in the setting of metric spaces. After showing some important examples of geodesic metric spaces (which will be used through this talk), we shall define the concept of firmly nonexpansive mappings and we shall prove the existence, under mild conditions, of periodic points and fixed points for this class of mappings. Some of these results unify and generalize previous ones. We shall give a result relative to the $\Delta$convergence to a fixed point of Picard iterates for firmly nonexpansive mappings, which is obtained from the asymptotic regularity of this class of iterates. Moreover, we shall get an effective rate of asymptotic regularity for firmly nonexpansive mappings (this result is new, as far as we know, even in linear spaces). Finally, we shall apply our results to a minimization problem. More precisely, we shall prove the $\Delta$convergence to a minimizer of a proximal pointlike algorithm when applied to a convex proper lower semicontinuous function defined on a CAT(0) space.
 [Permanent link]
