The Nonlinear Ergodic Theorem for Asymptotically Nonexpansive Mappings in Banach Spaces
The Nonlinear Ergodic Theorem for Asymptotically Nonexpansive Mappings in Banach Spaces
Let $X$ be a uniformly convex Banach space with a Frechet differentiable norm, $C$ a bounded closed convex subset of $X$, and $T:C \to C$ an asymptotically nonexpansive mapping. It is shown that for each $x$ in $C$, the sequence $\{ {T^n}x\}$ is weakly almost-convergent to a fixed point $y$ …