Iterative solution of nonlinear equations involving set-valued uniformly accretive operators
Let E be a real normed linear space and let A : E --> 2(E) be a uniformly continuous and uniformly quasi-accretive multivalued map with nonempty closed values such that the range of (I - A) is bounded and the inclusion f epsilon Ax has a solution x* epsilon E. It is proved that Ishikawa and Mann type iteration processes converge strongly to x*. Further, if T : E H 2E is a uniformly continuous and uniformly hemicontractive set-valued map with bounded range and a fixed point x* E E, it is proved that both the Mann and Ishikawa type iteration processes converge strongly to x*. The strong convergence of these iteration processes with errors is also proved. (C) 2001 Elsevier Science Ltd. All rights reserved.
iterations uniformly continuous uniformly quasi-accretive uniformly hemicontractive normed spaces