Viscosity Approximtion of Fixed Points for a Finite Family of Nonexpansive Mappings

Let E be a uniformly smooth Banach space,C a closed convex subset of E. Let f:C→C be a contractive mapping,T_1,T_2,…,T_N be a finite family of nonexpansive mappings of C into itself such that the set ∩ from i=1 to N(F(T_i)≠Ф) of common fixed points of T_1,T_2,…,T_N is nonempty.It is shown by using viscosity approximation methods,some sufficient and necessary conditions for the iterative sequence {x_n} defined by (1.4) converges strongly to a common fixed point of T_1,T_2,…,T_N.The results presented in this paper extend and improve some recent results.