Iterative solutions of nonlinear accretive operator equations in arbitrary Banach spaces

Abstract

Suppose E is an arbitrary real Banach space and K is a nonempty closed convex and bounded subset of E. Suppose T : K —>• K is a uniformly continuous strong pseudocontraction. It is proved that the Mann and the Ishikawa iteration methods converge strongly to the unique fixed point of T. Furthermore, our results also hold for the slightly more general class of strictly hemicontractive maps. Related results deal with the iterative approximation of solutions of accretive operator equations in arbitrary real Banach spaces. MIRAMARE TRIESTE April 1996 Permanent address: Department of Mathematics, University of Nigeria, Nsukka, Nigeria.