Fixed points of nonexpansive potential operators in Hilbert spaces

In this paper, we show the impact of certain general results by the author on the topic described in the title. Here is a sample: Let (X, <., .>) be a real Hilbert space and let T : X -> X be a nonexpansive potential operator. Then, the following alternative holds: either T has a fixed point, or, for each sphere S centered at 0, the restriction to S of the functional x -> integral(1)(0) < T(sx), x > ds has a unique global maximum towards which each maximizing sequence in S converges.