A mean ergodic theorem for nonexpansive mappings in Hadamard spaces (Q2043701)
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| Language | Label | Description | Also known as |
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| English | A mean ergodic theorem for nonexpansive mappings in Hadamard spaces |
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A mean ergodic theorem for nonexpansive mappings in Hadamard spaces (English)
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3 August 2021
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The authors generalize the Baillon nonlinear ergodic theorem to the case of nonexpansive mappings in Hadamard (nonpositive curvature complete metric) spaces. Namely, they shows that the Karcher means of the iterations converges weakly to a fixed point of the mapping, which is supposed to exist. This result is also extended for \(1\)-parameter continuous semigroups of contractions.
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Hadamard spaces
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nonexpansive mappings
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fixed points
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Karcher mean
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mean ergodic theorem
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weak convergence
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\(1\)-parameter semigroups of contractions
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