Viscosity approximation methods for nonexpansive mappings and inverse-strongly monotone mappings in Hilbert spaces

Abstract

Let C be a closed convex subset of a Hilbert space H. Let f is a contraction on C. Let S be a nonexpansive mapping of C into itself and A be an α-inverse-strongly monotone mapping of C into H. Assuming that F(S)∩VI(C,A)≠φ, and x0=x∈C, in this paper we introduce the iterative process xn+1=αnf(xn)+βnxn+γn(μSxn+(1−μ)(PC(I−λnA)yn)), where yn=PC(I−λnA)xn. We prove that {xn} and {yn} converge strongly to the same point z∈F(S)∩VI(C,A). As its application, we give a strong convergence theorem for nonexpansive mapping and strictly pseudo-contractive mapping in a Hilbert space.