Dorian Popa

On the stability of the linear functional equation in a single variable on complete metric groups

In this paper we obtain a result on Hyers–Ulam stability of the linear functional equation in a single variable

Hyers–Ulam stability of the linear differential operator with nonconstant coefficients

f(\varphi (x)) = g(x) \cdot f(x)

Hyers―Ulam stability of Euler's equation

f(φ(x))=g(x)·f(x) on a complete metric group.

Note on nonstability of the linear recurrence

Let X be a Banach space over the field ℝ or ℂ, a1,...,ap ∈ ℂ, and (bn)n≥0) a sequence in X. We investigate the Hyers-Ulam stability of the linear recurrence xn+p = a1xn+p-1 + ⋯ + ap-1xn+1 + apxn + bn, n ≥ 0, where x0,x1,...,xp-1 ∈ X.

Remarks on stability of linear recurrence of higher order

Abstract We obtain some stability results for the linear differential operator of order one in Banach spaces. As a consequence we derive a result on Hyers–Ulam stability for the linear differential operator of higher order with nonconstant coefficients.

Full length article: The Fréchet functional equation with application to the stability of certain operators

Abstract We obtain a result on stability of the linear differential equation of higher order with constant coefficients in Aoki–Rassias sense. As a consequence we obtain the Hyers–Ulam stability of the above mentioned equation. A connection with dynamical sytems perturbation is established.

Note on nonstability of the linear functional equation of higher order

Abstract We prove that Euler’s equation x 1 ∂ u ∂ x 1 + x 2 ∂ u ∂ x 2 + ⋯ + x n ∂ u ∂ x n = α u , characterising homogeneous functions, is stable in Hyers–Ulam sense if and only if α ∈ R ∖ { 0 } .

Remarks on Stability of the Linear Functional Equation in Single Variable

We prove a non-stability result for linear recurrences with constant coefficients in Banach spaces. As a consequence we obtain a complete solution of the problem of the Hyers-Ulam stability for those congruences in the complex Banach space.