Convergence Theorems for Fixed Points of Multivalued Strictly Pseudocontractive Mappings in Hilbert Spaces

Abstract

Let $K$ be a nonempty, closed, and convex subset of a real Hilbert space $H$. Suppose that $T:K\to {\mathrm{2}}^K$ is a multivalued strictly pseudocontractive mapping such that $F(T)\ne \mathrm{\varnothing }$. A Krasnoselskii-type iteration sequence $\{x_n\}$ is constructed and shown to be an approximate fixed point sequence of $T$; that is, ${\text{lim}}_{n\to \mathrm{\infty }}d(x_n,T{x}_n)=\mathrm{0}$ holds. Convergence theorems are also proved under appropriate additional conditions.