Extreme fixed points of operator LFT, applications to the Königs problem Original Research Article

We proceed with our study of the Königs problem (KE-problem), which was initiated and developed by several authors. We show that a wide class of fractional-linear mappings with a fixed point on the boundary of the unit operator ball DD have the KE-property. This means that each mapping from this class can be included in some semigroup of holomorphisms of DD which is continuous in the topology of locally uniform (over DD) convergence.