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The nonlinear ergodic theorem for asymptotically nonexpansive mappings in Banach spaces. (English) Zbl 0781.47045
The authors prove some results related to the weak almost convergence of the sequence of an asymptotically non-expansive mapping in a uniformly convex Banach space that has a Frechet differentiable norm. They also extend the results to a nonlinear ergodic theorem.
MSC:
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47H09Mappings defined by “shrinking” properties
47H20Semigroups of nonlinear operators