Stability and hyperstability of orthogonally ring $*$-$n$-derivations and orthogonally ring $*$-$n$-homomorphisms on $C^*$-algebras

Fuzzy Stability of Ring Homomorphisms and Ring Derivations on Fuzzy Banach Algebras

In this paper, we establish the Hyers–Ulam–Rassias stability of ring homomorphisms and ring derivations on fuzzy Banach algebras.

$n$-Jordan homomorphisms on C-algebras

Let $nin mathbb{N}$. An additive map $h:Ato B$ between algebras $A$ and $B$ is called $n$-Jordan homomorphism if $h(a^n)=(h(a))^n$ for all $ain A$. We show that every $n$-Jordan homomorphism between commutative Banach algebras is a $n$-ring homomorphism when $n < 8$. For these cases, every involutive $n$-Jordan homomorphism between commutative C-algebras is norm continuous.

Nearly Ring Homomorphisms and Nearly Ring Derivations on Non-Archimedean Banach Algebras

and Applied Analysis 3 Moreover, Bourgin 15 and Găvruţa 16 have considered the stability problem with unbounded Cauchy differences see also 17–27 . On the other hand, J. M. Rassias 28–33 considered the Cauchy difference controlled by a product of different powers of norm. However, there was a singular case; for this singularity a counterexample was given by Găvruţa 34 . This stability phenomeno...

Hyers-Ulam-Rassias stability of n-Jordan *-homomorphisms on C*-algebras

In this paper, we introduce n-jordan homomorphisms and n-jordan *-homomorphisms and Also investigate the Hyers-Ulam-Rassiasstability of n-jordan *-homomorphisms on C*-algebras.

Orthogonally Additive Polynomials on C*-algebras

Let A be a C*-algebra which has no quotient isomorphic to M2(C). We show that for every orthogonally additive scalar nhomogeneous polynomials P on A such that P is Strong* continuous on the closed unit ball of A, there exists φ in A∗ satisfying that P (x) = φ(x), for each element x in A. The vector valued analogue follows as a corollary.

Stability of Homomorphisms and Generalized Derivations on Banach Algebras