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Fixed point theorem for nonexpansive semigroup on Banach space


Authors: Wataru Takahashi and Doo Hoan Jeong
Journal: Proc. Amer. Math. Soc. 122 (1994), 1175-1179
MSC: Primary 47H20; Secondary 47H09, 47H10
DOI: https://doi.org/10.1090/S0002-9939-1994-1223268-8
MathSciNet review: 1223268
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Abstract: Let C be a nonempty closed convex subset of a uniformly convex Banach space, and let S be a semitopological semigroup such that $ {\text{RUC}}(S)$ has a left invariant submean. Then we prove a fixed point theorem for a continuous representation of S as nonexpansive mappings on C.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1223268-8
Keywords: Fixed point, nonexpansive mapping, mean
Article copyright: © Copyright 1994 American Mathematical Society

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