Related papers: Fixed Point Sets in Digital Topology, 2
Freezing sets and cold sets have been introduced as part of the theory of fixed points in digital topology. In this paper, we introduce a generalization of these notions, the limiting set, and examine properties of limiting sets.
Cold sets and freezing sets belong to the theory of (approximate) fixed points for continuous self-maps on digital images. We study some properties of cold sets for digital images in the digital plane, and we examine some relationships…
In this paper, we examine some properties of the fixed point set of a digitally continuous function. The digital setting requires new methods that are not analogous to those of classical topological fixed point theory, and we obtain results…
In this article, we investigate some properties of the coincidence point set of digitally continuous maps. Following the Rosenfeld graphical model which seems more combinatorial than topological, we expect to achieve results that might not…
We continue the study of freezing sets in digital topology, introduced in [2]. We show how to find a minimal freezing set for a "thick" convex disk X in the digital plane Z^2. We give examples showing the significance of the assumption that…
This paper continues a series discussing flaws in published assertions concerning fixed points in digital images.
We continue the study of freezing sets for digital images introduced in [4, 2, 3]. We prove methods for obtaining freezing sets for digital images (X, c_i) for X \subset Z^2 and i \in {1, 2}. We give examples to show how these methods can…
We develop new tools for the construction of fixed point sets in digital topology. We define excludable points and show that these may be excluded from all freezing sets. We show that articulation points are excludable. We also present…
The topic of fixed points in digital metric spaces continues to draw publications with assertions that are incorrect, incorrectly proven, trivial, or incoherently stated. We continue the work of our earlier papers that discuss publications…
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…
We investigate indeterminate points in discrete integrable system. They appear in singularity confinement phenomenon naturally. We develop a method to analyse indeterminate points of dynamical maps and using this method we clarify behaviour…
Several recent papers in digital topology have sought to obtain fixed point results by mimicking the use of tools from classical topology, such as complete metric spaces and homotopy invariant fixed point theory. We show that in many cases,…
In this paper we study the existence and uniqueness of fixed points of a class of mappings defined on complete, (sequentially compact) cone metric spaces, without continuity conditions and depending on another function.
Cone and suspension constructions have been introduced in digital topology, modeled on those of classical topology. For digital cones and suspensions, and for some related digital images, we find (m, n)-limiting sets; especially (0,…
We establish a fixed-point theorem for the face maps that consist in deleting the $i$th entry of an ordered set. Furthermore, we show that there exists random finite sets of integers that are almost invariant under such deletions.…
Among other results, the paper gives new mapping theorems and new fixed point property theorems for inverse limits of inverse sequences of compact metric spaces with upper semicontinuous set-valued bonding functions. We also revisit the…
This paper continues a series discussing flaws in published assertions concerning fixed points in digital metric spaces.
We study the approximate fixed point property (AFPP) for continuous single-valued functions and for continuous multivalued functions in digital topology. We extend what is known about these notions and discuss errors that have appeared in…
With a view towards providing tools for analyzing and understanding digitized images, various notions from algebraic topology have been introduced into the setting of digital topology. In the ordinary topological setting, invariants such as…
We generalize the fixed-point property for discrete groups acting on convex cones given by Monod in \cite{monod} to topological groups. At first, we focus on describing this fixed-point property from a functional point of view, and then we…