Fixed Point of a Pseudocontractive Map in a Banach Space

The Ishikawa iterative sequence is shown to converge strongly to the unique fixed point of a Pseudocontractive map in uniformly smooth real Banach space. The convergence of the Iterative sequence to this unique fixed of the pseudocontractive map is guaranteed whether or not the pseudocontractive map is Lipschitzian or has a bounded range. The Uniqueness of a fixed point of such a Pseudocontractive map is also discussed.