Strong Convergence Theorems for Zeros of Bounded Maximal Monotone Nonlinear Operators

Abstract

An iteration process studied by Chidume and Zegeye 2002 is proved to converge strongly to a solution of the equation $Au=0$ where A is a bounded m-accretive operator on certain real Banach spaces E that include $L_p$ spaces The iteration process does not involve the computation of the resolvent at any step of the process and does not involve the projection of an initial vector onto the intersection of two convex subsets of E, setbacks associated with the classical proximal point algorithm of Martinet 1970, Rockafellar 1976 and its modifications by various authors for approximating of a solution of this equation. The ideas of the iteration process are applied to approximate fixed points of uniformly continuous pseudocontractive maps.