Generalized viscosity approximation methods for nonexpansive mappings
Peichao Duan, Songnian He · Fixed Point Theory and Applications · 2014
We combine a sequence of contractive mappings and propose a generalized viscosity approximation method. One side, we consider a nonexpansive mapping S with the nonempty fixed point set defined on a nonempty closed convex subset C of a real Hilbert space H and design a new iterative method to approximate some fixed point of S, which is also a unique solution of the variational inequality. On the other hand, using similar ideas, we consider N nonexpansive mappings with the nonempty common fixed point set defined on a nonempty closed convex subset C. Under reasonable conditions, strong convergence theorems are proven. The results presented in this paper improve and extend the corresponding results reported by some authors recently. MSC:47H09, 47H10, 47J20, 47J25.