Convergence theorems for total asymptotically nonexpansive mappings.
In this paper we establish a dual weak convergence theorem for the Ishikawa iteration process for nonexpansive mappings in a reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm, and then apply this result to study the problem of the weak convergence of the iteration process.
We define a spectrum for Lipschitz continuous nonlinear operators in Banach spaces by means of a certain kind of "pseudo-adjoint" and study some of its properties.