Jong Su An

On the Stability of Quadratic Functional Equations

Let 𝑋,𝑌 be vector spaces and 𝑘 a fixed positive integer. It is shown that a mapping 𝑓(𝑘𝑥

Isomorphisms and Derivations in Lie

We investigate isomorphisms between C*-algebras, Lie C*-algebras, and JC*-algebras, and derivations on C*-algebras, Lie C*-algebras, and JC*-algebras associated with the Cauchy–Jensen functional equation 2f((x

C^*

AbstractIn this paper, we prove the Hyers-Ulam stability of the following function inequalities: in Banach spaces.MSC:39B62, 39B52, 46B25.

-Algebras

Abstractwe prove the Hyers-Ulam-Rassias stability of -algebra homomorphisms and of generalized derivations on -algebras for the following Cauchy-Jensen functional equation , which was introduced and investigated by Baak (2006). The concept of Hyers-Ulam-Rassias stability originated from the stability theorem of Th. M. Rassias that appeared in (1978).

Additive Functional Inequalities in Banach Modules

We investigate Jordan -derivations on -algebras and Jordan -derivations on -algebras associated with the following functional inequality for some integer greater than 1. We moreover prove the generalized Hyers-Ulam stability of Jordan -derivations on -algebras and of Jordan -derivations on -algebras associated with the following functional equation for some integer greater than 1.

Stability of the Cauchy-Jensen Functional Equation in -Algebras: A Fixed Point Approach

We investigate Jordan -derivations on -algebras and Jordan -derivations on -algebras associated with the following functional inequality for some integer greater than 1. We moreover prove the generalized Hyers-Ulam stability of Jordan -derivations on -algebras and of Jordan -derivations on -algebras associated with the following functional equation for some integer greater than 1.

Jordan -Derivations on -Algebras and -Algebras

It is shown that every almost positive linear mapping h : A ! B of a Banach ⁄-algebra A to a Banach ⁄-algebra B is a positive linear operator when h(rx) = rh(x)(r > 1) holds for all x 2 A, and that every almost linear mapping h : A ! B of a unital C ⁄ -algebra A to a unital C ⁄ -algebra B is a positive linear operator when h(2 n u ⁄ y) = h(2 n u) ⁄ h(y) holds for all unitaries u 2 A, all y 2 A, and all n = 0,1,2,..., by using the Hyers-Ulam-Rassias stability of functional equations. Under a more weak condition than the condition as given above, we prove that every almost linear mapping h : A ! B of a unital C⁄-algebra A to a unital C⁄-algebra B is a positive linear operator. It is applied to investigate states, center states and center-valued traces.

Jordan∗-Derivations onC∗-Algebras andJC∗-Algebras

We investigate Jordan -derivations on -algebras and Jordan -derivations on -algebras associated with the following functional inequality for some integer greater than 1. We moreover prove the generalized Hyers-Ulam stability of Jordan -derivations on -algebras and of Jordan -derivations on -algebras associated with the following functional equation for some integer greater than 1.