The convergence property of ishikawa iteration schemes in noncompact subsets of hilbert spaces and its applications to complementarity theory

In this paper, we prove a theorem of convergence of Ishikawa iteration schemes in Hilbert spaces for nonexpansive and completely continuous mapping with at least one fixed point. Then, we apply this theorem to solve some nonlinear complementarity problems defined by a completely continuous field ƒ and a closed pointed convex cone in K in a special Hilbert space H.