Digital Fixed Points, Approximate Fixed Points, and Universal Functions

TL;DR

This paper explores fixed point and approximate fixed point properties of digitally continuous functions, revealing new results and their connection to universal functions within digital images.

Contribution

It provides new insights into fixed point properties of digital images and links these properties to universal functions, expanding understanding in digital topology.

Findings

Digital images often have approximate fixed point properties.

Relationships between universal functions and AFPP are established.

Additional results on fixed points of digitally continuous functions.

Abstract

A. Rosenfeld introduced the notion of a digitally continuous function between digital images, and showed that although digital images need not have fixed point properties analogous to those of the Euclidean spaces modeled by the images, there often are approximate fixed point properties of such images. In the current paper, we obtain additional results concerning fixed points and approximate fixed points of digitally continuous functions. Among these are several results concerning the relationship between universal functions and the approximate fixed point property (AFPP).