Remarks on Fixed Point Assertions in Digital Topology, 11

TL;DR

This paper critiques recent publications on fixed point assertions in digital topology, highlighting errors, trivialities, and incoherent statements in the field.

Contribution

It provides a critical analysis of existing literature, clarifying misconceptions and emphasizing the need for rigorous proofs in digital fixed point theory.

Findings

Identifies common errors in fixed point assertions

Highlights trivial or incoherent claims in digital topology

Calls for more rigorous proofs in the field

Abstract

The topic of fixed points in digital metric spaces has drawn yet more publications with assertions that are incorrect, incorrectly proven, trivial, or incoherently stated. We discuss publications with bad assertions concerning fixed points of self-functions on digital images, as in some of our previous papers.