Strong Convergence Theorems for Zeros of Bounded Maximal Monotone Nonlinear Operators

Abstract

An iteration process studied by Chidume and Zegeye 2002 is proved to convergestronglyto a solution of the equationAu=0whereAis a boundedm-accretive operator on certain real Banach spacesEthat includeLpspaces2≤p<∞.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 ofE, setbacks associated with the classicalproximal point algorithmof 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.