This article deals with the iteration scheme
where is a strictly pseudocontractive mapping with , is a nonempty closed convex subset of a real -uniformly smooth Banach space (), , is a bounded sequence in , are sequences in , and the following conditions are satisfied: , , ().
Recall that a mapping with domain is called strictly pseudocontractive if there exists such that for all there exists satisfying
here is the normalized duality (multi)mapping. The constant is a minimal constant for which the inequality holds.
The main result is that the iterates converge strongly to a fixed point of if and only if is bounded and .