David Shoikhet

Nonlinear semigroups, fixed points, and geometry of domains in banach spaces

# Mappings in Metric and Normed Spaces # Differentiable and Holomorphic Mappings in Banach Spaces # Hyperbolic Metrics on Domains in Complex Banach Spaces # Some Fixed Point Principles # The Denjoy-Wolff Fixed Point Theory # Generation Theory for One-Parameter Semigroups # Flow-Invariance Conditions # Stationary Points of Continuous Semigroups # Asymptotic Behavior of Continuous Flows # Geometry of Domains in Banach Spaces

Filtration of Semi-complete Vector Fields Revisited

In this note we use a technique based on subordination theory in order to continue the study of filtration theory of semi-complete vector fields.

A Burns–Krantz-type Theorem for Pseudo-contractive Mappings

In this note we prove a rigidity result for pseudo-contractive mappings on the unit disk of the complex plane in the spirit of the Burns–Krantz theorem. As an auxiliary assertion, for pseudo-contractive mappings fixing the origin and 1, we establish an inequality connecting the first derivatives at these points.