Viscosity iteration method in CAT(0) spaces without the nice projection property

Attapol Kaewkhao, Bancha Panyanak, Suthep Suantai
2015 Journal of Inequalities and Applications  
A complete CAT(0) space X is said to have the nice projection property (property N for short) if its metric projection onto a geodesic segment preserves points on each geodesic segment, that is, for any geodesic segment L in X and x, y ∈ X, m ∈ [x, y] implies P L (m) ∈ [P L (x), P L (y)], where P L denotes the metric projection from X onto L. In this paper, we prove a strong convergence theorem of a two-step viscosity iteration method for nonexpansive mappings in CAT(0) spaces without the
more » ... ion on the property N . Our result gives an affirmative answer to a problem raised by Piatek (Numer. Funct. Anal. Optim. 34:1245-1264 , 2013 .
doi:10.1186/s13660-015-0801-6 fatcat:hntmokxncve4djdb2og5wc3cl4