Coincidence and Self-coincidence of Many Maps between Digital Images

TL;DR

This paper extends properties of coincidence and fixed point sets from pairs of digitally continuous maps to multiple maps, exploring the effects of rigidity and digital topology on these sets and comparing with classical Nielsen results.

Contribution

It generalizes coincidence properties to multiple digitally continuous maps and examines the influence of rigidity and digital topology on these sets.

Findings

Generalized coincidence point set properties for multiple maps

Analyzed the impact of rigidity on coincidence sets

Compared digital topology results with classical Nielsen theory

Abstract

The aim of this paper is to generalize some of the properties and results regarding both the coincidence point set and the common fixed point set of any two digitally continuous maps to the case of several (more than two) digitally continuous mappings. Moreover, we study how rigidity may affect these coincidence and homotopy coincidence point sets. Also, we investigate whether an established result by Staecker in Nielsen classical topology regarding the coincidence set for many maps still remains valid in the digital topological setting.