The approximation to a fixed point

TL;DR

This paper discusses methods to reach or approximate fixed points of strictly contracting mappings in spherically complete ultrametric spaces, extending understanding of fixed point existence and approximation in such mathematical structures.

Contribution

It introduces approaches for approximating fixed points in ultrametric spaces, providing insights into convergence methods beyond existence proofs.

Findings

Fixed points exist for strictly contracting mappings in spherically complete ultrametric spaces.

Methods for reaching or approximating these fixed points are outlined.

The paper enhances understanding of fixed point approximation in non-Archimedean analysis.

Abstract

In a spherically complete ultrametric space, a strictly contracting mapping has a fixed point. We indicate in this paper how this fixed point can either be reached or approximated.