Analytic functions over valued fields

Abstract

Let K be a non-archimedean, non-trivially (rank 1) valued complete field. B, B0 denote the closed and open unit ball of K respectively. Necessary and sufficient conditions for analytic functions defined on B, B0 with values in K to be injective, necessary and sufficient conditions for fixed points, the problem of subordination are studied in this paper.

Keywords

• non-archimedean valuation
• analytic
• univalent
• subordination
• fixed points.