The aim of this paper is to consider the Hyers-Ulam stability of a class of parabolic equation { ∂u ∂t − a 2∆u+ b · ∇u+ cu = 0, (x, t) ∈ Rn × (0,+∞), u(x, 0) = φ(x), x ∈ Rn. We conclude that (i) it is Hyers-Ulam stable on any finite interval; (ii) if c 6= 0, it is Hyers-Ulam stable on the semi-infinite interval; (iii) if c = 0, it is not Hyers-Ulam stable on the semi-infinite interval by using ...

Let X and Y be Hilbert C∗-modules over a C∗-algebra, and φ : X ×Y → [0,∞) be a function. A (not necessarily linear) mapping f : X → Y is called a φ-perturbed adjointable mapping if there exists a (not necessarily linear) mapping g : Y → X such that ‖〈f(x), y〉 − 〈x, g(y)〉‖ ≤ φ(x, y) (x ∈ X , y ∈ Y). In this paper, we investigate the generalized Hyers–Ulam–Rassias stability of adjointable mapping...

and Applied Analysis 3 Moreover, Bourgin 15 and Găvruţa 16 have considered the stability problem with unbounded Cauchy differences see also 17–27 . On the other hand, J. M. Rassias 28–33 considered the Cauchy difference controlled by a product of different powers of norm. However, there was a singular case; for this singularity a counterexample was given by Găvruţa 34 . This stability phenomeno...

In 1940, Ulam 1 gave a talk before the Mathematics Club of the University of Wisconsin in which he discussed a number of unsolved problems, containing the stability problem of homomorphisms as follows Let G1 be a group and let G2 be a metric group with the metric d ·, · . Given ε > 0, does there exist a δ > 0 such that if a mapping h : G1 → G2 satisfies the inequality d h xy , h x h y < δ for a...

&lt;p style='text-indent:20px;'&gt;In this paper, the Hyers-Ulam-Rassias stability of high-dimensional quaternion fuzzy dynamic equations with impulses is first considered on time scales. Some fundamental calculus results functions in space are established. Based it, some sufficient conditions obtained to guarantee impulsive case. Moreover, several examples provided show feasibility our main va...

moslehian  and mirmostafaee, investigated the fuzzystability problems for the cauchy additive functional equation, the jensen additivefunctional equation and the cubic functional equation in fuzzybanach spaces. in this paper, we investigate thegeneralized hyers–-ulam--rassias stability of the generalizedadditive functional equation with $n$--variables, in fuzzy banachspaces. also, we will show ...