In this paper, we study the Baker’s superstability for the following functional equation (E (K)) ∑ φ∈Φ ∫ K f(xkφ(y)k)dωK(k) = |Φ|f(x)f(y), x, y ∈ G where G is a locally compact group, K is a compact subgroup of G, ωK is the normalized Haar measure of K, Φ is a finite group of K-invariant morphisms of G and f is a continuous complex-valued function on G satisfying the Kannappan type condition, f...

In this paper, we investigate the stability and superstability of homomorphisms on C∗−ternary algebras associated with the functional equation f( x+ 2y + 2z 5 ) + f( 2x+ y − z 5 ) + f( 2x− 3y − z 5 ) = f(x).

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.

We study this and associated theorems in the context of a logmodular function algebra and, in particular, in the Banach algebra, H, of bounded analytic functions on D. Those multiplicative linear functionals (homomorphisms) on if which are in the weak* closure of some Stolz angle at 1 are called Stolz homomorphisms. We call a homomorphism h a Lindelof homomorphism provided h(f) = 0 whenever ess...

1Introduction: The generalized linear signal processing systems have been introduced and extensively studied by Oppenheim et al. [5] at the end of the 1960s. A generalized linear signal processing system consists of vector spaces for the input and output signal sets and a linear mapping, called the system transformation [5]. In their research, Oppenheim et al. have mainly focused on the impleme...

Let G and H be two groups. For simplicity, we denote by + the group operation in each of these groups. A function f : G → H is called a (group) homomorphism if for every x, y ∈ G it holds that f(x+ y) = f(x) + f(y). One important special case of interest is when H is a finite field and G is a vector space over this field; that is, G = H for some natural number m. In this case, a homomorphism f ...

This paper is part of a program initiated by Saharon Shelah to extend the model theory of first order logic to the nonelementary setting of abstract elementary classes (AECs). An abstract elementary class is a semantic generalization of the class of models of a complete first order theory with the elementary substructure relation. We examine the symmetry property of splitting (previously isolat...