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Nonlinear ergodic theorems for asymptotically almost nonexpansive curves in a Hilbert space

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  • Gang Li
  • Jong Kyu Kim

Abstract

We introduce the notion of asymptotically almost nonexpansive curves which include almost-orbits of commutative semigroups of asymptotically nonexpansive type mappings and study the asymptotic behavior and prove nonlinear ergodic theorems for such curves. As applications of our main theorems, we obtain the results on the asymptotic behavior and ergodicity for a commutative semigroup of non-Lipschitzian mappings with nonconvex domains in a Hilbert space.

Suggested Citation

  • Gang Li & Jong Kyu Kim, 2000. "Nonlinear ergodic theorems for asymptotically almost nonexpansive curves in a Hilbert space," Abstract and Applied Analysis, Hindawi, vol. 5, pages 1-12, January.
    • Handle: RePEc:hin:jnlaaa:840360
    DOI: 10.1155/S1085337500000312
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