Abstract
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).
Acknowledgements
The second author undertook this work when he was visiting the Abdus Salam International Centre for Theoretical Physics, Trieste, Italy, as a postdoctoral fellow.