Strong convergence theorems for common fixed points of uniformlyL-Lipschitzian pseudocontractive semi-groups
C.E. Chidume, Habtu Zegeye · Applicable Analysis · 2007
Let K be a nonempty closed convex subset of a uniformly convex real Banach space E which has uniformly Gâteaux differentiable norm. Let 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 un in K satisfying , where αn∈[0,1) and tn > 0 are real sequences satisfying appropriate conditions. Furthermore, {un } converges strongly to a fixed point of . Moreover, explicit iteration procedures which converge strongly to a fixed point of 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).