A Mean Ergodic Theorem for Nonlinear Semigroups which are Asymptotically Nonexpansive in the Intermediate Sense

@article{Kaczor2000AME,
  title={A Mean Ergodic Theorem for Nonlinear Semigroups which are Asymptotically Nonexpansive in the Intermediate Sense},
  author={Wiesława Kaczor and Tadeusz Kuczumow and Simeon Reich},
  journal={Journal of Mathematical Analysis and Applications},
  year={2000},
  volume={246},
  pages={1-27}
}
Abstract Let X be a uniformly convex Banach space such that its dual X* has the Kadec–Klee property, C a bounded closed convex subset of X, and T  = {T(t) : t ∈ [0, ∞)} a one-parameter nonlinear semigroup which is asymptotically nonexpansive in the intermediate sense. We show that every continuous almost orbit of T is weakly almost convergent to a common fixed point of T . A discrete version of our main result is also included. 
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