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Strong Ergodic Theorem for Asymptotically Almost Non-expansive Curves in Hilbert Spaces

Let C be a nonempty subset of a Hilbert space H,and G a commutative semi-topological semigroup.We first give the definition of asymptotically almost non-expansive curve u(·):G→C.Then we prove the strong ergodic theorem for asymptotically almost non-expansive curves.As applications,we obtain the strong ergodic theorem for the almost orbits of asymptotically non-expansive type semigroups without convexity,which extends and improves all the previous results.