Axioms, Volume 7, Issue 2

Anomalous waves and rogue events are closely associated with irregularities and unexpected events occurring at various levels of physics, such as in optics, in oceans and in the atmosphere. Mathematical modeling of rogue waves is a highly active fiel...

The notion of a neutrosophic quadruple $BCK/BCI$-number is considered, and a neutrosophic quadruple $BCK/BCI$-algebra, which consists of neutrosophic quadruple $BCK/BCI$-numbers, is constructed. Several properties are investigated, and a (positive implicat...

This paper aims to illustrate how SABO (Semi-Analytical method for Barrier Option pricing) is easily applicable for pricing floating strike Asian barrier options with a continuous geometric average. Recently, this method has been applied in the Black...

A nonlinear eigenvalue problem is generally described by an equation of the form $F(\lambda ,x)=0$, where $F(\lambda ,0)=0$ for all $\lambda$, and contains by definition two unknowns: the eigenvalue parameter $\lambda$ and the “nontrivial” vect...

Essentially, whenever a generalized hypergeometric series can be summed in terms of gamma functions, the result will be important as only a few such summation theorems are available in the literature. In this paper, we apply two identities of general...

We focus on the articles recently published in the special issue of Axioms devoted to “New Trends in Fuzzy Set Theory and Related Items”.

In recent years, the numerical solution of differential problems, possessing constants of motion, has been attacked by imposing the vanishing of a corresponding line integral. The resulting methods have been, therefore, collectively named (discrete)...

In this short paper, we aim at a qualitative framework for modeling multivariate decision problems where each alternative is characterized by a set of properties. To this extent, we consider convex spaces as underlying universes and make use of latti...

The $T_1$ -spaces induced by the pre-metric spaces along with many forms of triangle inequalities are investigated in this paper. The limits in pre-metric spaces are also studied to demonstrate the consistency of limit concept in the induced topo...

Technique for the order of preference by similarity to ideal solution (TOPSIS) and elimination and choice translating reality (ELECTRE) are widely used methods to solve multi-criteria decision making problems. In this research article, we present bip...

A class $\mathfrak{M}$ of coarse spaces is called a variety if $\mathfrak{M}$ is closed under the formation of subspaces, coarse images, and products. We classify the varieties of coarse spaces and, in particular, show that if a variety $\mathfrak{M}$ contains an unbound...

One of the main properties of solutions of nonlinear Caputo fractional neural networks is stability and often the direct Lyapunov method is used to study stability properties (usually these Lyapunov functions do not depend on the time variable). In c...

This article concerns the basic understanding of parabolic final value problems, and a large class of such problems is proved to be well posed. The clarification is obtained via explicit Hilbert spaces that characterise the possible data, giving exis...

Different abstract versions of entropy, encountered in science, are interpreted in the light of numerical representations of several ordered structures, as total-preorders, interval-orders and semiorders. Intransitivities, other aspects of entropy as...

This paper continues our earlier investigation, where a walk-on-spheres (WOS) algorithm for Monte Carlo simulation of the solutions of the Yukawa and the Helmholtz partial differential equations (PDEs) was developed by using the Duffin correspondence...

Using of the principle of subordination, we investigate some subordination and convolution properties for classes of multivalent functions under certain assumptions on the parameters involved, which are defined by a generalized fractional differinteg...

Relations between I-quasi-valuation maps and ideals in $BCK/BCI$ -algebras are investigated. Using the notion of an I-quasi-valuation map of a $BCK/BCI$ -algebra, the quasi-metric space is induced, and several properties are inves...

In this paper, we study the class of mixed-index time fractional differential equations in which different components of the problem have different time fractional derivatives on the left-hand side. We prove a theorem on the solution of the linear sy...

In this paper, using an infinite matrix of complex numbers, a modulus function and a lacunary sequence, we generalize the concept of $\mathcal{I}$ -sta...

For $i,j,k,l,m,n\in \{1,2,3,4\}$ , the notion of $\left(T\right(i,j),I(k,l),F(m,n\left)\right)$ -interval neutrosophic subalgebra in $BCK/BCI$ -algebra is introduced, and their properties and relations are investiga...

In this paper, by applying umbral calculus methods to generating functions for the combinatorial numbers and the Apostol type polynomials and numbers of order k, we derive some identities and relations including the combinatorial numbers, the Apostol...

The bipolar neutrosophic set is an important extension of the bipolar fuzzy set. The bipolar neutrosophic set is a hybridization of the bipolar fuzzy set and neutrosophic set. Every element of a bipolar neutrosophic set consists of three independent...

In this research article, we present a novel framework for handling intuitionistic fuzzy soft information by combining the theory of intuitionistic fuzzy soft sets with graphs. We introduce the notion of certain types of intuitionistic fuzzy soft gra...