Steepest descent method for equilibrium points of nonlinear systems with accretive operators

Let E be a real normed linear space and let A: E --> 2(E) be a bounded unif ormly continuous phi-strongly accretive multi-valued map with nonempty clos ed values such that the inclusion 0 is an element of Ax has a solution x* i s an element of E. It is proved that both the Ishikawa and the Mann iterati on processes are bounded and converge strongly to x*. Related results deal with the convergence of the iteration processes to fixed points of phi-stro ngly pseudocontractive maps and the iterative solution of the equation 0 is an element of x + Fx for an accretive map F. Furthermore, the Ishikawa and Mann iteration methods with errors are discussed and proofs are sketched o n how our theorems extend to these methods. Our method of proof is of indep endent interest. (C) 2000 Academic Press.