The purpose of this article is to investigate lacunary ideal convergence sequences in neutrosophic normed space (NNS). Also, an original notion, named sequence NNS, defined. $% \mathcal{I}$-limit points and $\mathcal{I}$-cluster NNS have been examined. Furthermore, Cauchy $\mathcal{I}$-Cauchy are introduced some properties these notions studied.

The classical result on well-posedness of Cauchy problem for the linear ordinary differential system with the distributional right-hand side and smooth matrix of coefficients plays fundamental role in many applications of distribution theory to ordinary and partial differential equations. In the present paper we generalize this result to the case of system (0.1) x − A(t)x = f, where f is a dist...

The object of this paper is to determine Hyers–Ulam–Rassias stability concerning the Jensen functional equation in intuitionistic fuzzy normed space (IFNS) by using the fixed point method. Further, we establish stability of the Cauchy functional equation in IFNS.

We consider a Cauchy problem for a semilinear heat equation with absorption. The initial datum of the problem is bounded and its infimum is positive. We study solutions which do not vanish in the total space at the vanishing time; they vanish only at space infinity.

The aim of this paper is to establish the existence of solutions and some properties of set solutions for a Cauchy problem with causal operator in a separable Banach space.

We consider Cauchy problem for three-dimensional Navier-Stokes system with periodic boundary conditions with initial data from the space of pseudo-measures Φ(α). We provide global existence and uniqueness of the solution for sufficiently small initial data.

The Cauchy problem for the damped Boussinesq equation with small initial data is considered in two space dimensions. Existence and uniqueness of its classical solution is proved and the solution is constructed in the form of a series. The major term of its long-time asymptotics is calculated explicitly and a uniform in space estimate of the residual term is given.

We extend the results of a work by L. Hörmander [9] concerning the resolution of the characteristic Cauchy problem for second order wave equations with regular first order potentials. The geometrical background of this work was a spatially compact spacetime with smooth metric. The initial data surface was spacelike or null at each point and merely Lipschitz. We lower the regularity hypotheses o...

Consider the B-valued probability space (A, E,B), where A is a tracial von Neumann algebra. We extend the theory of operator valued free probability to the algebra of affiliated operators Ã. For a random variable X ∈ Ã we study the Cauchy transform GX and show that the von Neumann algebra (B ∪ {X}) ′′ can be recovered from this function. In the case where B is finite dimensional, we show that, ...