Theorems of Denjoy–Wolff type

Using the Kobayashi distance, we first establish a version of the Denjoy–Wolff theorem for a bounded and strictly convex domain in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbb{C}}^k}$$\end{document} . Next, we prove analogous results for semigroups of holomorphic mappings and the resolvents of their generators. Finally, we obtain theorems of Denjoy–Wolff type for families of holomorphic retracts of the open unit ball in a complex, reflexive, and strictly convex Banach space.