ITERATIVE ALGORITHM FOR FIXED POINTS OF MULTI-VALUED PSEUDO-CONTRACTIVE MAPPINGS IN BANACH SPACES

Let q > 1 and let E be a q-uniformly smooth real Banach space and K be a nonempty, closed and convex subset of E. Let CB(K) be the collection of all closed and bounded subsets of K. Suppose that T : K -> CB(K) is a multi-valued bounded continuous pseudo-contractive mapping with a nonempty fixed point set. A new iteration scheme is constructed and the corresponding sequence {x(n)} is proved to converge strongly to a fixed point of T under appropriate conditions on the iteration parameters. Our theorems are significant improvements on several important recent results.