Iterative solution of nonlinear equations of accretive and pseudocontractive types

Let E be a real uniformly smooth Banach space. Let A: D(A) = E → 2^E be an accretive operator that satisfies the range condition and A^-1(0) ≠. Let {λ_n} and {θ_n} be two real sequences satisfying appropriate conditions, and for z ∈ E arbitrary, let the sequence {x_n} be generated from arbitrary x₀ ∈ E by x_n+1 = x_n - λ_n (u_n + θ_n(x_n - z)), u_n ∈ Ax_n, ≥ 0. Assume that {u_n} is bounded. It is proved that {x_n} converges strongly to Some x* ∈ A^-1 (0). Furthermore, if K is a nonempty closed convex subset of E and T: K → K is a bounded continuous pseudocontractive map with F (T) := {Tx = x} ≠, it is proved that for arbitrary z ∈ K, the sequence {x_n} generated from x₀ ∈ K by x_n+1 = x_n - λ_n ((I - T)x_n + θ_n (x_n - z)), n ≥ 0,) where {λ_n} and {θ_n} are real sequences satisfying appropriate conditions, converges strongly to a fixed point of T.