Global Iterative Schemes for Accretive Operators

Let E be a real q-uniformly smooth Banach space and A : E 2 E be an m-accretive operator which satisfies a linear growth condition of the form Ax cŽ1 x . for some constant c 0 and for all x E. It is proved that if two real sequences n4 and n4 satisfy appropriate conditions, the sequence xn4 generated from arbitrary x0 E by xn 1 xn nŽun nŽ xn z..; un Axn n 0, con- verges strongly to some x A 1Ž0.. Furthermore, if E is a reflexive Banach space with a uniformly Gˆateaux differentiable norm, and if every weakly compact convex subset of E has the fixed-point property for nonexpansive mappings and A : DŽ A. E 2 E is m-accretive, then for arbitrary, z, x0 E the sequence xn4 defined by xn 1 nŽun 1 nŽ xn 1 z.. xn en, for un Axn, where en E is such that Ý en n 0, converges strongly to some x A 1Ž0..