APPROXIMATING FIXED-POINTS OF PHI-HEMICONTRACTIVE MAPPINGS BY THE ISHIKAWA ITERATION PROCESS WITH ERRORS IN UNIFORMLY SMOOTH BANACH-SPACES

Let E be a uniformly smooth Banach space and T : E --> E be a continuo us and strongly phi-hemicontractive mapping. This paper proves that, u nder suitable conditions, the Ishikawa iterative sequence with errors strongly converges to the unique fixed point of T. The related result deals with the strong convergence of the Ishikawa iterative sequence w ith errors to the unique solution of the equation Tx = f when T : E -- > E is phi-strongly accretive. These results generalize the results of Ding [1] into more general phi-hemicontractive operators and extend a recent paper written by Osilike [2] in two ways. (i) The Lipschitzian continuity is replaced by the continuity on mapping T. (ii) If the er rors u(n) = upsilon(n) = 0, for all n is an element of N, our theorems of this paper extend results df Osilike [2] to the more general class of real uniformly smooth Banach spaces. (C) 1998 Elsevier Science Ltd . All rights reserved.