Strong convergence theorems for fixed points of asymptotically pseudocontractive semi-groups

Let K be a nonempty closed convex and bounded subset of a real Banach space E. Let T = {T (t): t ∈ R+} be a strongly continuous uniformly asymptotically regular and uniformly L-Lipschitzian semi-group of asymptotically pseudocontractive mappings from K into K. Then for a given u ∈ K there exists a sequence {yn} ∈ K satisfying the equation yn = (1−αn)(T (tn))nyn+αnu for each n ∈ N, where αn ∈ (0, 1) and tn > 0 satisfy appropriate conditions. Suppose further that E is uniformly convex and has uniformly Gâteaux differentiable norm, under suitable conditions on the mappings T , the sequence {yn} converges strongly to a fixed point of T . Furthermore, an explicit sequence {xn} generated from x1 ∈ K by xn+1 := (1 − λn)xn +λn(T (tn))nxn − λnθn(xn − x1) for all integers n 1, where {λn}, {θn} are positive real sequences satisfying appropriate conditions, converges strongly to a fixed point of T .  2004 Elsevier Inc. All rights reserved.