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

Let q>1 and let K be a nonempty, closed and convex subset of a q-uniformly smooth real Banach space E. Let T:K→CB(K) be a multi-valued strictly pseudo-contractive map with a nonempty fixed point set. A Krasnoselskii-type iteration sequence {xn} is constructed and proved to be an approximate fixed point sequence of T, i.e., limn→∞d(xn,Txn)=0. 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.