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.

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.

In this paper, we study Hyers–Ulam and generalized Hyers–Ulam–Rassias stability of a system hyperbolic partial differential equations using Gronwall’s lemma Perov’s theorem.

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.

We show that  higher derivations on a Hilbert$C^{*}-$module associated with the Cauchy functional equation satisfying generalized Hyers--Ulam stability.  

In this paper, the author established the general solution and generalized Ulam Hyers Rassias stability of n− dimensional Arun-additive functional equation f ( nx0 ± n ∑

In this paper, we define a generalized additive set-valued functional equation, which is related to the following generalized additive functional equation: f (x 1 + · · · + x l) = (l – 1)f x 1 + · · · + x l–1 l – 1 + f (x l) for a fixed integer l with l > 1, and prove the Hyers-Ulam stability of the generalized additive set-valued functional equation.

We study the generalized Ulam-Hyers stability, the well-posedness, and the limit shadowing of the fixed point problem for new type of generalized contraction mapping, the so-called α-β-contraction mapping. Our results in this paper are generalized and unify several results in the literature as the result of Geraghty (1973) and the Banach contraction principle.

a unital $c^*$ -- algebra $mathcal a,$ endowed withthe lie product $[x,y]=xy- yx$ on $mathcal a,$ is called a lie$c^*$ -- algebra. let $mathcal a$ be a lie $c^*$ -- algebra and$g,h:mathcal a to mathcal a$ be $bbb c$ -- linear mappings. a$bbb c$ -- linear mapping $f:mathcal a to mathcal a$ is calleda lie $(g,h)$ -- double derivation if$f([a,b])=[f(a),b]+[a,f(b)]+[g(a),h(b)]+[h(a),g(b)]$ for all ...