An example for a one-parameter nonexpansive semigroup

Abstract

We give one example for a one-parameter nonexpansive semigroup. This example shows that there exists a one-parameter nonexpansive semigroup $\left\{T\left(t\right):t\ge 0\right\}$ on a closed convex subset $C$ of a Banach space $E$ such that ${\text{lim}}_{t\to \infty }\Vert \left(1/t\right){\int }_0^{t}T\left(s\right)xds-x\Vert =0$ for some $x\in C$, which is not a common fixed point of $\left\{T\left(t\right):t\ge 0\right\}$.