Related papers: Remarks on Fixed Point Assertions in Digital Topol…
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.…
Digital topology is part of the ongoing endeavour to understand and analyze digitized images. With a view to supporting this endeavour, many notions from algebraic topology have been introduced into the setting of digital topology. But some…
In this note we document a gap in an argument in the above paper, and point to new work in the literature giving a complete proof of the main result.
In this paper, three Computational Topology methods (namely effective homology, persistent homology and discrete vector fields) are mixed together to produce algorithms for homological digital image processing. The algorithms have been…
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…
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…
In this paper we present some fixed-figure theorems as a geometric approach to the fixed-point theory when the number of fixed points of a self-mapping is more than one. To do this, we modify the Jleli-Samet type contraction and define new…
This work aims to define the concept of manifold, which has a very important place in the topology, on digital images. So, a general perspective is provided for two and three-dimensional imaging studies on digital curves and digital…
The main purpose of this work is to extend the properties of multivalued transformations to the integral type transformations and to obtain the existence of fixed points under F-contraction. In addition, the results of this study were…
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.
We correct some oversights in the paper "A spectral sequence for stratified spaces and configuration spaces of points" by the second named author. In particular we explain that an additional hypothesis should be added to Theorem 4.15 in…
A gap in the proof of Theorem 3.5 in the paper ``A new iteration process for approximation of common fixed points for finite families of total asymtotically nonexpansive mappings". Int. J. Math. Math. Sci. vol. 2009,…
This paper provides an overview of modern digital geometry and topology through mathematical principles, algorithms, and measurements. It also covers recent developments in the applications of digital geometry and topology including image…
The concept of quasi-partial b-metric-like spaces is being introduced and studied with the help of topology. Examples are also discussed to support the results. Some fixed point theorems are proved in the setting of quasi-partial…
In this study, we improve the topological complexity computations on digital images with introducing the digital topological complexity computations of a surjective and digitally continuous map between digital images. We also reveal…
In this paper, we will continue the investigation of Waring's problem, and give further improvements.
We shall generalize the concept of $z=(1-t)x\oplus ty$ to $n$ times which contains to verifying some their properties and inequalities in CAT(0) spaces. In the sequel with introducing of $\alpha$-nonexpansive mappings, we obtain some fixed…
Topological features play an essential role in ensuring geometric plausibility and structural consistency in image analysis tasks such as segmentation and skeletonization. However, integrating topology-preserving learning based on simple…
Banach's fixed point theorem in linear n-normed space is being developed. Also, we present several theorems on fixed points in linear n-normed space.
We discuss some results concerning fixed point equations in the setting of topological *-algebras of unbounded operators. In particular, an existence result is obtained for what we have called {\em weak $\tau$ strict contractions}, and some…