An example for a one-parameter nonexpansive semigroup - Tomonari Suzuki (Abstract and Applied Analysis)
We give one example for a one-parameter nonexpansive semigroup. This example shows that there exists a one-parameter nonexpansive semigroup {T(t):t≥0} on a closed convex subset C of a Banach space E such that limt→∞‖(1/t)∫0tT(s)xds−x‖=0 for some x∈C, which is not a common fixed point of {T(t):t≥0}.