Related papers: Remarks on Fixed Point Assertions in Digital Topol…
In our paper "Dendroidal sets as models for homotopy operads" (J. Topol. 4 (2011), no. 2, 257-299, and arXiv:0902.1954), we made the wrong claim about the behaviour of the tensor product with respect to cofibrations of dendroidal sets. We…
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 consider 9 natural tightness conditions for topological spaces that are all variations on countable tightness and investigate the interrelationships between them. Several natural open problems are raised.
We establish fixed point theorems for nonlinear contractions on a metric space (not essentially complete) endowed with an arbitrary binary relation. Our results extend, generalize, modify and unify several known results especially those…
This supplementary information contains detailed derivations, comparison to experiment, and discussion of other miscellaneous issues omitted from the main text.
In this short paper, we prove fixed point theorems for nonexpansive mappings whose domains are unbounded subsets of Banach spaces. These theorems are generalizations of Penot's result in [Proc. Amer. Math. Soc., 131 (2003), 2371--2377].
In this paper, we show that the stability analysis in the paper A note on stability of fractional logistic maps, Appl. Math. Lett. 125 (2022) 107787 is incorrect and repeat a proof of a theorem on the convergence of a convolution of the…
v2: An additional assumption was added in Theorem 4.8. In order to show that a connected abelian group is admissible on the site of locally compact spaces we must in addition assume that it is locally topologically divisible. This condition…
In this paper we introduce FG- coupled fixed point, which is a generalization of coupled fixed point for nonlinear mappings in partially ordered complete metric spaces. We discuss existence and uniqueness theorems of FG- coupled fixed…
We use a simple geometric argument and small cancellation properties of link groups to prove that alternating links are non-trivial. This proof uses only classic results in topology and combinatorial group theory.
Transformations of digital spaces preserving local and global topology play an important role in thinning, skeletonization and simplification of digital images. In the present paper, we introduce and study contractions of simple pair of…
Counterfactual explanations (CFEs) provide actionable recourse, but most methods assume a static framework with fixed data and a trained classifier. This assumption breaks in evolving data environments, such as data streams, where online…
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.…
The weakly contractive metric type fixed point result in Berinde [Nonlinear Anal. Forum, 9 (2004), 45-53] is "almost" covered by the related altering metric one due to Khan et al [Bull. Austral. Math. Soc., 30 (1984), 1-9]. Further…
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.
The aim of this paper is to discuss Penot's problem on a generalization of Caristi's fixed point theorem. We settle this problem in the negative and we present some new theorems on the existence of fixed points of set-valued mappings in…
In this paper, a detrimental mathematical mistake is pointed out in the proof of \textit{Theorem 1} presented in the paper\textit{ [Generalization of the gradient method with fractional order gradient direction, J. Franklin Inst., 357…
This is an appendix to our paper "An update of the Hirsch Conjecture" (arXiv:0907.1186), containing proofs of some of the results and comments that were omitted in it.
We discuss some easy statements dealing with linear inhomogeneous Diophantine approximation. Surprisingly, we did not find some of them in the literature.
We summarize recent progress in the understanding of fixed point resolution for conformal field theories. Fixed points in both coset conformal field theories and non-diagonal modular invariants which describe simple current extensions of…