Axioms, Volume 8, Issue 2

We will prove the generalized Hyers–Ulam stability and the hyperstability of the additive functional equation f(x₁ + y₁, x₂ + y₂, …, x_n + y_n) = f(x₁, x₂, … x_n) + f(y₁, y₂, …, y_n). By restricting the domain of a mapping f that satisfies the inequality...

In this paper, we use the orthogonal system of the Jacobi polynomials as a tool to study the Riemann–Liouville fractional integral and derivative operators on a compact of the real axis. This approach has some advantages and allows us to comple...

Different results regarding different integro-differentials are usually not properly generalized, as they often do not satisfy some of the constraints. The field of fuzzy integro-differentials is very rich these days because of their different applic...

In this paper, we propose a new approach to constructing similarity measures using the entropy measure for Interval-Valued Intuitionistic Fuzzy Sets. In addition, we provide several illustrative examples to demonstrate the practicality and effectiven...

In this short survey, we aim to underline the importance of the non-unique fixed point results in various abstract spaces. We recall a brief background on the topic and we combine, collect and unify several existing non-unique fixed points in the lit...

The problem of complete controllability of a linear time-invariant singularly-perturbed system with multiple commensurate non-small delays in the slow state variables is considered. An approach to the time-scale separation of the original singularly-...

In this manuscript, we introduce almost b-metric spaces and prove modifications of fixed point theorems for Reich and Hardy–Rogers type contractions. We present an approach generalizing some fixed point theorems to the case of almost b-metric s...

Some well known results from the existing literature are extended and generalized via new contractive type mappings in fuzzy metric spaces. A non trivial supporting example is also provided to demonstrate the validity of the obtained results.

The aim of this paper is to establish some new $(p,q)$ -calculus of Hermite–Hadamard inequalities for the double integral and refinements of the Hermite–Hadamard inequality for $(p,q)$ -differentiable convex functions.

We first provide a best proximity point result for quasi-noncyclic relatively nonexpansive mappings in the setting of dualistic partial metric spaces. Then, those spaces will be endowed with convexity and a result for a cyclic mapping will be obtaine...

In this article, we show that there are homeomorphisms of plane continua whose conjugacy class is residual and have the shadowing property.

Numerous higher-order methods with derivative evaluations are accessible in the literature for computing multiple zeros. However, higher-order methods without derivatives are very rare for multiple zeros. Encouraged by this fact, we present a family...

In this review, I will discuss the historical importance of “The Significance of the New Logic” by Quine. This is a translation of the original “O Sentido da Nova Lógica” in Portuguese by Carnielli, Janssen-Lauret, and...

In this paper, we obtain a new series representation for the generalized Bose–Einstein and Fermi–Dirac functions by using fractional Weyl transform. To achieve this purpose, we obtain an analytic continuation for these functions by genera...

The purpose of this note is to provide an expository introduction to some more curious integral formulas and transformations involving generating functions. We seek to generalize these results and integral representations which effectively provide a...

This paper is a continuation of a previous article that appeared in AXIOMS in 2018. A Euler’s formula for hyperbolic functions is considered a consequence of a unifying point of view. Then, the unification of Jordan, Lie, and associative algebr...

In this paper, the authors obtain some new sufficient conditions for the oscillation of all solutions of the fourth order delay differential equations. Some new oscillatory criteria are obtained by using the generalized Riccati transformations and co...

The authors of the above mentioned paper specify that the considered class of one-step symmetric Hermite-Obreshkov methods satisfies the property of conjugate-symplecticity up to order $p+r,$ where $r=2$ and p is the order of the me...

Mobile robot motion planning in an unstructured, static, and dynamic environment is faced with a large amount of uncertainties. In an uncertain working area, a method should be selected to address the existing uncertainties in order to plan a collisi...

Under some conditions, an asymptotic solution containing boundary functions was constructed in a paper by Vasil’eva and Butuzov (Differ. Uravn. 1970, 6(4), 650–664 (in Russian); English transl.: Differential Equations 1971, 6, 499–5...

In this manuscript, we utilize the concept of modified $\omega$ -distance mapping, which was introduced by Alegre and Marin [Alegre, C.; Marin, J. Modified $\omega$ -distance on quasi metric spaces and fixed point theorems on complete quasi m...

In this paper, a simple family of one-point iterative schemes for approximating the solutions of nonlinear equations, by using the procedure of weight functions, is derived. The convergence analysis is presented, showing the sufficient conditions for...

Currently, we are in the digital era, where robotics, with the help of the Internet of Things (IoT), is exponentially advancing, and in the technology market we can find multiple devices for achieving these systems, such as the Raspberry Pi, Arduino,...

For an $\alpha$ -expansive homeomorphism of a compact space we give an elementary proof of the following well-known result in topological dynamics: A sufficient condition for the homeomorphism to have the shadowing property is that it has the $$...

We analyze the notion of reproducing pairs of weakly measurable functions, a generalization of continuous frames. The aim is to represent elements of an abstract space Y as superpositions of weakly measurable functions belonging to a space $Z:=$...

By using the monomiality principle and general results on Sheffer polynomial sets, the differential equation satisfied by several old and new polynomial sets is shown.

In this manuscript, we design two classes of parametric iterative schemes to solve nonlinear problems that do not need to evaluate Jacobian matrices and need to solve three linear systems per iteration with the same divided difference operator as the...

In the setting of Minkowski set-valued operations, we study generalizations of the difference for (multidimensional) compact convex sets and for fuzzy sets on metric vector spaces, extending the Hukuhara difference. The proposed difference always exi...

In this paper, by introducing the concept of generalized Ćirić-type weak $({\varphi }_g,\mathcal{R})$ -contraction, we prove some common fixed point results in partial metric spaces endowed with binary relation $\mathcal{R}$ . We also deduce some useful consequence...

In this paper, we provide a formal proof of the existence of a polynomial solution of fixed degree for a second-order divided-difference equation of the hypergeometric type on non-uniform lattices, generalizing therefore previous work proving existen...

The displacement problem of linear elastostatics in bounded and exterior domains with a non-regular boundary datum $\mathit{a}$ is considered. Precisely, if the elastic body is represented by a domain of class $C^k(k\ge 2)$ of ${\mathbb{R}}^3$...

In this paper, we prove that on any contact manifold $(M,\xi )$ there exists an arbitrary $C^{\infty }$ -small contactomorphism which does not admit a square root. In particular, there exists an arbitrary $C^{\infty }$ -small contacto...

We show, using the spectral Galerkin method together with compactness arguments, the existence and uniqueness of the periodic strong solutions for the magnetohydrodynamic-type equations with inhomogeneous boundary conditions. Furthermore, we study th...

In this work, new Bäcklund transformations (BTs) for generalized Liouville equations were obtained. Special cases of Liouville equations with exponential nonlinearity that have a multiplier that depends on the independent variables and first-ord...

This paper lies in the framework of axiomatic non-standard analysis based on the non-standard arithmetic axiomatic theory. This arithmetic includes actual infinite numbers. Unlike the non-standard model of arithmetic, this approach does not take mode...

In this article, I consider local solutions of the 3D Navier–Stokes equations and its properties such as an existence of global and smooth solution, uniform boundedness. The basic role is assigned to a special invariant class of solenoidal vect...

This study deals with the problem of pricing compound options when the underlying asset follows a mixed fractional Brownian motion with jumps. An analytic formula for compound options is derived under the risk neutral measure. Then, these results are...

In this paper, we present four product operations to construct cryptographic boolean functions from smaller ones with predictable Walsh spectrum. A lot of cryptographic properties of boolean functions can be presented by their Walsh spectrum. In our...

This manuscript presents a new two-step weighted Newton’s algorithm with convergence order five for approximating solutions of system of nonlinear equations. This algorithm needs evaluation of two vector functions and two Frechet derivatives pe...

In this paper, we examine the finite mixture (FM) model with a flexible class of two-piece distributions based on the scale mixtures of normal (TP-SMN) family components. This family allows the development of a robust estimation of FM models. The TP-...