NONLINEAR ERGODIC THEOREMS FOR WIDELY MORE GENERALIZED HYBRID MAPPINGS IN HILBERT SPACES
In this paper, using strongly asymptotically invariant nets, we first obtain some properties of widely more generalized hybrid mappings ina Hilbert space. Then, using the idea of mean convergence by Shimizu and Takahashi [24, 25], we prove a nonlinear ergodic theorem for widely more generalized hybrid mappings in a Hilbert space. This generalizes the Kawasaki and Takahashi nonlinear ergodic theorem.
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