Krasnoselskii-type algorithm for fixed points of multi-valued strictly pseudo-contractive mappings

Let and let K be a nonempty, closed and convex subset of a q-uniformly smooth real Banach space E. Let be a multi-valued strictly pseudo-contractive map with a nonempty fixed point set. A Krasnoselskii-type iteration sequence is constructed and proved to be an approximate fixed point sequence of T, i.e., . This result is then applied to prove strong convergence theorems for a fixed point of T under additional appropriate conditions. Our theorems improve several important well-known results. MSC:47H04, 47H06, 47H15, 47H17, 47J25.