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Proceedings of the American Mathematical Society

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A nonlinear ergodic theorem for an amenable semigroup of nonexpansive mappings in a Hilbert space


Author: Wataru Takahashi
Journal: Proc. Amer. Math. Soc. 81 (1981), 253-256
MSC: Primary 47H20; Secondary 47H09, 47H10
DOI: https://doi.org/10.1090/S0002-9939-1981-0593468-X
MathSciNet review: 593468
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Abstract: We prove a nonlinear ergodic theorem for noncommutative semigroups of nonexpansive mappings in a Hilbert space. Furthermore, we give a necessary and sufficient condition for a noncommutative semigroup to have a fixed point.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0593468-X
Keywords: Ergodic theorem, amenable semigroup, nonexpansive mapping, fixed point
Article copyright: © Copyright 1981 American Mathematical Society