Axioms, Volume 15, Issue 1

Some properties on large contractions in metric spaces are proven. In particular, such contractions are proven to be asymptotically regular. In addition, if the metric space is complete, then the sequences that they generate are bounded, Cauchy, and...

We introduce the concept of the modularity of an abelian variety defined over the rational number field extending the modularity of an elliptic curve. We discuss the modularity of an abelian variety over $\mathbb{Q}$. We conjecture that a simple abelian variety...

In this paper, we describe all Nijenhuis operators on 2-dimensional complex pre-Lie algebras and 3-dimensional complex associative algebras. As an application, using these operators, we obtain solutions to the classical Yang-Baxter equation on the co...

In this paper, for any real number λ, we transform the complete max-plus semiring ${\mathbb{R}}_{\infty }$ into a commutative, complete, additively idempotent semiring ${\mathbb{R}}_{\infty }^{\lambda }$, called the lower λ-truncation of ${\mathbb{R}}_{\infty }$. It is obtained by remov...

We propose a novel design approach for pinning control of a dynamical network that achieves synchronization despite switching between arbitrary topologies. Unlike existing approaches, we consider weighted, directed, and even unconnected topologies as...

This study focuses on the Modus Tollens (MT) property induced by discrete uninorms. Specifically, we identify the set of necessary and sufficient criteria for a discrete implication function to comply with this logical property. This rule of inferenc...

Dragonfly networks $D(n,h)$ are a class of interconnection topologies widely used for large-scale high-performance computing (HPC) systems. In such networks, path connectivity serves as a fundamental metric for evaluating fault tolerance and operationa...

We give several generalizations of a known theorem from complex analysis, namely the univalence on the boundary theorem. Starting from a purely topological result (Theorems 1 and 11), we obtain univalence conditions for Sobolev mappings.

This research explores two novel geometric concepts—nearly convex points and locally nearly uniformly convex points within the frameworks of Banach spaces and Orlicz spaces equipped with the Luxemburg norm. First, we establish the general chara...

We consider the Poisson stable solutions and their exponential attractiveness for the linear difference equation $z(n+1)=Az\left(n\right)+g\left(n\right)$ and semi-linear difference equation $z(n+1)=Az\left(n\right)+G(n,z(n\left)\right).$ Via Shcherbakov’s comparability principle, we show th...