Viscosity approximation methods for nonexpansive mappings in CAT(0) spaces are studied. Consider a nonexpansive self-mapping of a closed convex subset of a CAT(0) space . Suppose that the set Fix of fixed points of is nonempty. For a contraction on and , let be the unique fixed point of the contraction . We will show that if is a CAT(0) space satisfying some property, then converge strongly to a fixed point of which solves some variational inequality. Consider also the iteration process , where is arbitrary and for , where . It is shown that under certain appropriate conditions on converge strongly to a fixed point of which solves some variational inequality.
"Strong Convergence of Viscosity Approximation Methods for Nonexpansive Mappings in CAT(0) Spaces." J. Appl. Math. 2012 (SI03) 1 - 11, 2012. https://doi.org/10.1155/2012/421050