Approximation of fixed points of strongly pseudocontractive mappings in uniformly smooth Banach spaces (Q884193)

The author proves the following result. Let \(E\) be a real uniformly smooth Banach space, \(K\) be a nonempty closed convex subset of \(E\), and the map \(T: K \to K\) be continuous and strongly pseudocontractive. Then the Ishikawa iteration scheme converges to the unique fixed point of \(T\). The author buttresses his result with an example of a strongly pseudocontractive map \(T:=T_{1} + T_{2}\) which is neither Lipschitzian nor has a bounded range.