C. Moore et Bvc. Nnoli, Iterative solution of nonlinear equations involving set-valued uniformly accretive operators, COMPUT MATH, 42(1-2), 2001, pp. 131-140
Let E be a real normed linear space and let A : E --> 2(E) be a uniformly c
ontinuous and uniformly quasi-accretive multivalued map with nonempty close
d values such that the range of (I - A) is bounded and the inclusion f epsi
lon Ax has a solution x* epsilon E. It is proved that Ishikawa and Mann typ
e iteration processes converge strongly to x*. Further, if T : E H 2E is a
uniformly continuous and uniformly hemicontractive set-valued map with boun
ded range and a fixed point x* E E, it is proved that both the Mann and Ish
ikawa type iteration processes converge strongly to x*. The strong converge
nce of these iteration processes with errors is also proved. (C) 2001 Elsev
ier Science Ltd. All rights reserved.