... point theorems for new nonlinear mappings in a Hilbert spaces. J Nonlinear Convex Anal. 11,79–88 (2010)17. Takahashi, W, Yao, JC: Fixed point theorems and ergodic theorems for nonlinear mappings ... has a fixed point. Since then, the fixed point the ory for single-valued and multivalued mappings in CAT(0) spaces has been rapidlydeveloped, and many papers have appeared (e.g., see [3-6] and ... nonexpansive mapping if d(Tx, Ty) ≤ d(x, y)forallx, y Î C.A point x Î C iscalledafixedpointofT if Tx = x.LetF(T)denotethesetoffixedpoints of T.Now, we introduce the following nonlinear mappings on CAT(0)...