In this work, we present sufficient conditions in order to establish different types of Ulam stabilities for a class higher integro-differential equations. particular, consider new kind stability, the σ-semi-Hyers-Ulam which is some sense between Hyers–Ulam and Hyers–Ulam–Rassias stabilities. These result from application Banach Fixed Point Theorem, by applying specific generalization Bielecki ...

In this paper, we investigate the Hyers-Ulam stability of additive functional equations of two forms: of “Jensen” and “Jensen type” in the framework of multi-normed spaces. We therefore provide a link between multi-normed spaces and functional equations. More precisely, we establish the Hyers-Ulam stability of functional equations of these types for mappings from Abelian groups into multi-norme...

In this paper, we prove the generalized Hyers–Ulam stability of a quadratic and quartic functional equation in intuitionistic fuzzy Banach spaces.

We prove the generalized Hyers-Ulam stability of the one-dimensional wave equation, u(tt) = c(2)u(xx), in a class of twice continuously differentiable functions.

We solve the inhomogeneous Chebyshev’s differential equation and apply this result to obtain a partial solution to the Hyers-Ulam stability problem for the Chebyshev’s differential equation.

In this paper, we prove the generalized Hyers–Ulam stability of homomorphisms and (θ, φ)-derivations on a ring R into a Banach R-bimodule M.

We will apply a fixed point method for proving the Hyers–Ulam stability of the functional equation f(x+ y) = f(x)f(y) f(x)+f(y) .

We apply the Luxemburg–Jung fixed point theorem in generalized metric spaces to study the Hyers–Ulam stability for two functional equations in a single variable.

We study the generalized Hyers-Ulam stability of the functional equation f[x1,x2,x3]= h(x1+x2+x3). 2000 Mathematics Subject Classification. 39B22, 39B82.

Problem 1.1. Given a metric group (G,·,d), a positive number ε, and a mapping f : G→ G which satisfies the inequality d( f (xy), f (x) f (y)) ≤ ε for all x, y ∈ G, do there exist an automorphism a of G and a constant δ depending only on G such that d(a(x), f (x)) ≤ δ for all x ∈G? If the answer to this question is affirmative, we say that the equation a(xy) = a(x)a(y) is stable. A first answer ...