Approximation of fixed points of weakly contractive nonself maps in Banach spaces

Let K be a closed convex subset of a real uniformly smooth Banach space E. Suppose K is a nonexpansive retract of E with P as the nonexpansive retraction. Let T : K → E be a d-weakly contractive map such that a fixed point x* ∈ int(K) of T exists. It is proved that a descent-like approximation sequence converges strongly to x*. Furthermore, if K is a nonempty closed convex subset of an arbitrary real Banach space and T:K → K is a uniformly continuous d-weakly contractive map with F(T) := (x ∈ K: Tx = x) ≠ Ø, it is proved that a descent-like approximation sequence converges strongly to x* ∈ F(T).