Refine
Language
- English (4) (remove)
Is part of the Bibliography
- yes (4) (remove)
Keywords
- Analytic extension (1)
- Angular derivatives (1)
- Composition operators (1)
- Holomorphic map (1)
- Holomorphic mappings (1)
- Newton method (1)
- Non-linear semigroups (1)
- Semigroup (1)
- Unit disk (1)
- composition operator (1)
Institute
We prove a theorem on separation of boundary null points for generators of continuous semigroups of holomorphic self-mappings of the unit disk in the complex plane. Our construction demonstrates rather strikingly the particular role of the binary operation au broken vertical bar given by 1/ f au broken vertical bar g = 1/f + 1/g on generators.
In this paper we study the convergence of continuous Newton method for solving nonlinear equations with holomorphic mappings in complex Banach spaces. Our contribution is based on a recent progress in the geometric theory of spirallike functions. We prove convergence theorems and illustrate them by numerical simulations.