In this paper, we establish the generalized Hyers–Ulam–Rassias stability of homomorphisms between ternary algebras associted to the generalized Jensen functional equation rf( sx+ty r ) = sf(x) + tf(y).

In this paper, we establish the generalized Hyers–Ulam–Rassias stability of C-ternary ring homomorphisms associted to the Trif functional equation d · C d−2f( x1 + · · ·+ xd d ) + C d−2 d ∑

The Hyers–Ulam–Rassias stability of the conditional quadratic functional equation of Pexider type f (x+y)+f (x−y) = 2g(x)+2h(y), x ⊥ y is proved where ⊥ is the orthogonality in the sense of Rätz.

In this paper, the solution and the Hyers–Ulam stability of the following quadratic type functional equation k ∑ i=2 ∑ "j∈{−1,1} f (x1 + "jxi) = 2(k − 1)f(x1) + 2 k ∑

We show that generalizations of some (classical) results on the Hyers-Ulam stability of functional equations, in several variables, can be very easily derived from a simple result on stability of a functional equation in single variable.

In this paper we obtain a result on Hyers-Ulam stability of the linear functional equation in a single variable f(φ(x)) = g(x) · f(x) on a complete metric group.

We prove the generalized Hyers-Ulam-Rassias stability of a partitioned functional equation. It is applied to show the stability of algebra homomorphisms between Banach algebras associated with partitioned functional equations in Banach algebras.

Abstract The Laplace transform method is applied in this article to study the semi-Hyers-Ulam-Rassias stability of a Volterra integro-differential equation order n, with convolution-type kernel. This kind extends original Hyers-Ulam whose originated 1940. A general integral formulated first, and then some particular cases (polynomial function exponential function) for from kernel are considered.

We will apply the successive approximation method forproving the Hyers--Ulam stability of a linear integral equation ofthe second kind.

Mathematical modeling helps us to better understand different natural phenomena. Modeling is most of the times based on consideration appropriate equations (or systems equations). Here, differential are well-known be very useful instruments when building mathematical models - specially because that use derivatives offers several interpretations associated with real life laws. Differential class...