Strong convergence theorems for common fixed points of uniformly L-Lipschitzian pseudocontractive semi-groups

Let K be a nonempty closed convex subset of a uniformly convex real Banach space E which has uniformly Gâteaux differentiable norm. Let (Formula presented.) be a strongly continuous uniformly L-Lipschitzian semi-group of pseudocontractive mappings from K into E satisfying the weakly inward condition with a nonempty common fixed point set. Then, for a given u∈K, there exists a unique point u _n in K satisfying (Formula presented.), where α _n ∈[0,1) and t _n > 0 are real sequences satisfying appropriate conditions. Furthermore, {u _n } converges strongly to a fixed point of (Formula presented.). Moreover, explicit iteration procedures which converge strongly to a fixed point of (Formula presented.) are constructed. A corollary of this result gives an affirmative answer to a recent question posed in Suzuki (2003, Proceedings of the American Mathematical Society, 131, 2133–2136).