An affirmative answer to the open questions on the viscosity approximation methods for nonexpansive mappings in CAT(0) spaces
Shih-Sen Chang, Lin Wang, Gang Wang, Lijuan Qin · The Journal of Nonlinear Sciences and Applications · 2016
We prove a strong convergence theorem of a two-step viscosity iteration method for nonexpansive mappings in CAT(0) spaces without the nice projection property \(\mathbb{N}\) and the restriction of the contraction constant \(k \in [0; \frac{1}{2} )\). Our result gives an affrrmative answer to the open questions raised by Piatek [B. Piatek, Numer. Funct. Anal. Optim., 34 (2013), 1245-1264], and Kaewkhao et al. [A. Kaewkhao, B. Panyanak, S. Suantai, J. Inequal. Appl., 2015 (2015), 9 pages].