Convergence of paths for pseudo-contractive mappings in Banach spaces
Claudio H. Morales, Jong Soo Jung · Proceedings of the American Mathematical Society · 2000
Let X X be a real Banach space, let K K be a closed convex subset of X X , and let T T , from K K into X X , be a pseudo-contractive mapping (i.e. ( λ − 1 ) (\lambda -1) ‖ u − v ‖ ≤ ‖ ( λ I − T ) ( u ) − ( λ I − T ) ( v ) ‖ \|u-v\|\le \|(\lambda I-T)(u)-(\lambda I-T)(v)\| for all u , v ∈ K u,v\in K and λ > 1 ) \lambda >1) . Suppose the space X X has a uniformly Gâteaux differentiable norm, such that every closed bounded convex subset of K K