In this paper we introduce a notion of a non-Archimedean fuzzy norm and study the stability of the Cauchy equation in the context of non-Archimedean fuzzy spaces in the spirit of Hyers–Ulam–Rassias–Găvruţa. As a corollary, the stability of the Jensen equation is established. We indeed present an interdisciplinary relation between the theory of fuzzy spaces, the theory of non-Archimedean spaces ...

A model Boltzmann equation (see formulas (1.1.6) { (1.1.9) below) without Grad's angular cutoo assumption is considered. One proves 1. the instantaneous smoothing in both position and velocity variables by the evolution semigroup associated to the Cauchy problem for this model; 2. the derivation of the analogue of the Landau-Fokker-Planck equation in the limit when grazing collisions prevail.

Self-similar process with long-range dependence LRD , that is, fractional Gaussian noise fGn with LRD is a widely used model of Internet traffic. It is indexed by its Hurst parameterHfGn that linearly relates to its fractal dimensionDfGn. Note that, on the one hand, the fractal dimensionD of traffic measures local self-similarity. On the other hand, LRD is a global property of traffic, which is...

We study the Hamilton-Jacobi equations $H(x,Du,u)=0$ in $M$ and $\partial u/\partial t +H(x,D_xu,u)=0$ $M\times(0,\infty)$, where Hamiltonian $H=H(x,p,u)$ depends Lipschitz continuously on variable $u$. In framework of semicontinuous viscosity solutions due to Barron-Jensen, we establish comparison principle, existence theorem, representation formula as value functions for extended real-valued,...

let $r$ be a 2-torsion free ring and $u$ be a square closed lie ideal of $r$. suppose that $alpha, beta$ are automorphisms of $r$. an additive mapping $delta: r longrightarrow r$ is said to be a jordan left $(alpha,beta)$-derivation of $r$ if $delta(x^2)=alpha(x)delta(x)+beta(x)delta(x)$ holds for all $xin r$. in this paper it is established that if $r$ admits an additive mapping $g : rlongrigh...

n this paper we study the Hyers-Ulam-Rassias stability of Cauchyequation in Felbin's type fuzzy normed linear spaces. As a resultwe give an example of a fuzzy normed linear space such that thefuzzy version of the stability problem remains true, while it failsto be correct in classical analysis. This shows how the category offuzzy normed linear spaces differs from the classical normed linearspac...

Let $A$ be an unital alternative $*$-algebra. Assume that contains a nontrivial symmetric idempotent element $e$ which satisfies $xA \cdot e = 0$ implies $x and (1_A - e) 0$. In this paper, it is shown $\Phi$ nonlinear $*$-Jordan-type derivation on A if only additive $*$-derivation. As application, we get result $W^{*}$-algebras.