Hopfs ergodic theorem for nonlinear operators

  title={Hopfs ergodic theorem for nonlinear operators},
  author={Rainer Wittmann},
  journal={Mathematische Annalen},
  • Rainer Wittmann
  • Published 1991
  • Mathematics
  • 1 ~ T ' f (1) n + l i=0 are a.e. convergent. In this paper we will give a generalization of Hopfs theorem to a wide class of nonlinear operators. In the nonlinear situation, instead of being a contraction, one usually assumes that T is nonexpansive or at least norm decreasing on L I or L ~. The definition (1) can, of course, be literally generalized to nonlinear mappings, and the partial sums can be also defined inductively by Sof = f and S,, + 1 f = f + S,,(Tf). From the point of view of the… CONTINUE READING

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