Iterative Approximation with Errors for Lipschitz Strictly Pseudocontractive Mappings
Jin Mao-ming · Gongcheng shuxue xuebao · 2004
Suppose that K is a nonempty closed convex subset of an arbitrary real Banach space E. Let T : K → K be a Lipschitz strictly pseudocontractive mapping. In this paper, a new Ishikawa iterative sequence with errors which converges strongly to the unique ?xed point of T is given. The author presents a related result that the new Ishikawa iterative with errors converges to a solution of the nonlinear equation Tx = f when T is Lipschitz strongly accretive mapping. The results are obtained by removing the strict conditions of space E being uniformly smooth or P? uniformly smooth, the ∞ boundedness of K, lim αn = lim βn = 0 and αn ∞(s ). s n→∞ n→∞ n=0