A look at nonexpansive mappings in non-Archimedean vector spaces

Abstract

<jats:title>Abstract</jats:title>
<jats:p>In a spherically complete ultrametric space every nonexpansive self-mapping <jats:italic>T</jats:italic> has a fixed point ̄x or a minimal invariant ball <jats:italic>B</jats:italic>(̄x, <jats:italic>d</jats:italic>(̄x, <jats:italic>T</jats:italic>(̄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.</jats:p>