COMMON FIXED POINTS OF ONE-PARAMETER NONEXPANSIVE SEMIGROUPS
Tomonari Suzuki · Bulletin of the London Mathematical Society · 2006
In this paper, we show that the set of all common fixed points of a one-parameter nonexpansive semigroup is that of some single nonexpansive mapping. We next compare our result with Bruck's famous fixed-point theorem. We finally prove very simple convergence theorems to a common fixed point. In our discussion, we assume neither the strict convexity of the underlying space, nor the weak compactness of the domain of a nonexpansive semigroup. 2000 Mathematics Subject Classification 47H20 (primary), 47H10 (secondary).