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\\ less than or equal to c(1 + \\x\\) for some constant c > 0 and for all x is an element of E. It is proved that if two real sequences {lambda (n)} and {theta (n)} satisfy appropriate conditions, the sequence {x(n)} generated from arbitrary x(0) is an element of E by x(n+1) = x(n) - lambda (n)(u(n) + theta (n)(x(n) - z)); u(n) is an element of Ax(n) n greater than or equal to 0, converges strongly to some x* is an element of A(-1)(0). Furthermore, if E is a reflexive Banach space with a uniformly Gateaux differentiable norm, and if every weakly compact convex subset of E has the fixed-point property for nonexpansive mappings and A : D(A) := E --> 2(E) is m-accretive, then for arbitrary, z, x(0) is an element of E the sequence {x(n)} defined by x(n+1) + lambda (n)(u(n+1) + theta (n)(x(n+1) - z)) = x(n) + e(n), for u(n) is an element of Ax(n) where e(n) is an element of E is such that Sigma\\e(n)\\ < infinity For Alln greater than or equal to 0, converges strongly to some x* is an element of A(-1)(0). (C) 2001 Academic Press.