Modified Viscosity Iterations for Nonexpansive Mapping

Let H be a Hilbert space and X be a Banach space,C a nonempty closed convex subset of H or X,and T:C→C a nonexpansive mapping.Movitated by H.K.Xu′s studies of viscosity iterations for nonexpansive mapping,a new iterative method is generated as followed: where C is a closed convex subset of a Banach space and x0∈ C,xn+1= T[(1-αn)xn+ αn f(xn)],n≥0.We can get the strong convergence theorem both in Hilbert and Banach space.