Fixed point theorem for nonexpansive semigroup on Banach space

Takahashi, Wataru; Jeong, Doo Hoan

doi:10.1090/S0002-9939-1994-1223268-8

Fixed point theorem for nonexpansive semigroup on Banach space
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by Wataru Takahashi and Doo Hoan Jeong PDF

Proc. Amer. Math. Soc. 122 (1994), 1175-1179 Request permission

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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