Approximation of Solutions of Nonlinear Equations of Monotone and Hammerstein Type

Let X be a real uniformly smooth and uniformly convex Banach space with dual X *. Let A: X → X * be a bounded uniformly submonotone map. It is proved that a Mann-type approximation sequence converges strongly to Jx * where x * ∈ N(A). Furthermore, as an application of this result an iterative sequence which converges strongly to a solution of the Hammerstein equation u+KFu = 0 is constructed where, F:X→X* and K:X*→X are monotone-type mappings. No invertibility assumption is imposed on K. Moreover, neither K nor F need be compact. Finally, our method is of independent interest.