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New fixed point results are presented for ${\cal U}_c^{\kappa}(X,X)$ maps in extension type spaces.

Classical Analysis and ODEs · Mathematics 2007-05-23 Ravi P Agarwal , Jong Kyu Kim , Donal O'Regan

In the recent paper "Reparametrizations of continuous paths", J. Homotopy Relat. Struct. 2 (2007), 93-117 (with U. Fahrenberg), we performed a systematic investigation of reparametrizations of continuous paths in a Hausdorff space that…

Algebraic Topology · Mathematics 2009-02-16 Martin Raussen

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.

Metric Geometry · Mathematics 2021-07-16 Laurence Boxer

In this article, we investigate properties of digital H-spaces in the graph theoretic model of digital topology. As in prior work, the results obtained often depend fundamentally on the choice between NP$_1$ and NP$_2$ product adjacencies.…

Algebraic Topology · Mathematics 2024-08-20 Wayne A. Johnson , Dae-Woong Lee , P. Christopher Staecker

In this work we present an overview of approaches for the detection and attribution of synthetic images and highlight their strengths and weaknesses. We also point out and discuss hot topics in this field and outline promising directions…

Computer Vision and Pattern Recognition · Computer Science 2024-05-02 Diangarti Tariang , Riccardo Corvi , Davide Cozzolino , Giovanni Poggi , Koki Nagano , Luisa Verdoliva

The main purpose of this paper is to find the fixed point in such cases where existing literature remain silent. In this paper we introduce partial completeness, a new type of contraction and many other definitions. Using this approach the…

Functional Analysis · Mathematics 2018-03-23 Tawseef Rashid , Qamrul Haque Khan

We examine the relationship between convexity and the approximate fixed point property (AFPP) for digital images in Z^2.

Geometric Topology · Mathematics 2020-12-29 Laurence Boxer

The soft topological spaces and some their related concepts have stud- ied in [7]. In this paper, we introduce and study the notions of soft connected topological spaces after a review of preliminary definitions.

General Topology · Mathematics 2012-02-09 E. Peyghan , B. Samadi , A. Tayebi

This paper introduces the structure and axioms for a temporal digital topology (TDT) with the focus on digital connectedness, continuity and proximities in TDT spaces. Results are given for temporal digital adjacencies, connectedness and…

Algebraic Topology · Mathematics 2023-06-27 James Francis Peters , Tane Vergili

We consider fixed-point models for topological phases of matter formulated as discrete path integrals in the language of tensor networks. Such zero-correlation length models with an exact notion of topological invariance are known in the…

Strongly Correlated Electrons · Physics 2022-09-27 Andreas Bauer , Jens Eisert , Carolin Wille

A point of a digital space is called simple if it can be deleted from the space without altering topology. This paper introduces the notion simple set of points of a digital space. The definition is based on contractible spaces and…

Computer Vision and Pattern Recognition · Computer Science 2015-03-13 Alexander V. Evako

In this paper, we establish some fixed point theorems in ordered partial metric spaces. An example is given to illustrate our obtained results.

General Topology · Mathematics 2016-10-05 Hassen Aydi

In this note, we discuss some fixed point theorems for contractive self mappings defined on a $G$-metric spaces. More precisely, we give fised point theorems for mappings with a contractive iterate at a point.

General Topology · Mathematics 2017-02-24 Yaé Olatoundji Gaba

The recently introduced continuous Hopfield network (see Ramsauer et al.) exhibits large memorization capabilities, which manifest as attractive fixed points of its update rule -- a differentiable function consisting of two linear mappings…

Dynamical Systems · Mathematics 2026-04-06 Hans-Peter Beise

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.

Functional Analysis · Mathematics 2009-06-12 José R. Morales , Edixon Rojas

We add to our knowledge of the approximate fixed point property (AFPP) in digital topology. We show that a digital image that is a tree has the AFPP. Given two digital images (X, \kappa) and (Y, \lambda) that have the approximate fixed…

Geometric Topology · Mathematics 2020-04-08 Laurence Boxer

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,…

Geometric Topology · Mathematics 2025-07-22 Laurence Boxer

Fixed points represent equilibrium states, stability, and solutions to a range of problems. It has been an active field of research. In this paper, we provide an overview of the main branches of fixed point theory. We discuss the key…

History and Overview · Mathematics 2023-09-08 Firuz Kamalov , Ho Hon Leung

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…

Geometric Topology · Mathematics 2020-05-21 Laurence Boxer

We introduce a new type of homotopy relation for digitally continuous functions which we call ``strong homotopy.'' Both digital homotopy and strong homotopy are natural digitizations of classical topological homotopy: the difference between…

General Topology · Mathematics 2019-03-05 P. Christopher Staecker