Wolff–Denjoy theorems in geodesic spaces

We show a Wolff–Denjoy type theorem in complete geodesic spaces the spirit of Beardon's framework that unifies several results this area. In particular, it applies to strictly convex bounded domains R n or C with respect large class metrics including Hilbert's and Kobayashi's metrics. The are generalized 1-Lipschitz compact mappings infinite-dimensional Banach spaces.