An affirmative answer to the open questions on the viscosity approximation methods for nonexpansive mappings in CAT(0) spaces

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 N and the restriction of the contraction constant k ∈ [0, 1/2 ]. Our result gives an affirmative 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]