AFPP and Unions of Convex Disks in the Digital Plane

TL;DR

This paper investigates the approximate fixed point property (AFPP) in digital images, specifically focusing on conditions where unions of convex digital disks in the digital plane possess the AFPP, expanding theoretical understanding in digital topology.

Contribution

It provides new conditions under which unions of convex digital disks in the digital plane have the AFPP, extending previous results in digital topology.

Findings

Identifies conditions for unions of convex digital disks to have AFPP

Extends knowledge of AFPP in digital images in ^2

Builds on previous results to broaden applicability of AFPP

Abstract

We use results of [6] to enlarge our knowledge of the approximate fixed point property (AFPP) for digital images in $\mathbb{Z}^2$. In particular, we study conditions under which the union of two convex digital disks has the AFPP.