A look at nonexpansive mappings in non-Archimedean vector spaces

Abstract

In a spherically complete ultrametric space every nonexpansive self-mapping T has a fixed point ̄x or a minimal invariant ball B(̄x, d(̄x, T(̄x)). We show how we can approximate this fixed center ̄x in a non-Archimedean vector space. And, we give a synthetic study for increasing mapping in non-Archimedean local fields.

Keywords

• fixed centers
• increasing mappings
• nonexpansive mappings
• pseudo-order
• ultrametric spaces
• 47h09
• 32p05