Fixed Points and Hyers-Ulam-Rassias Stability of Cauchy-Jensen Functional Equations in Banach Algebras

We prove the Hyers-Ulam-Rassias stability of homomorphisms in real Banach algebras and of generalized derivations on real Banach algebras for the following Cauchy-Jensen functional equations: f(x+y/2+z)+f(x−y/2+z)=f(x)+2f(z), 2f(x+y/2+z)=f(x)+f(y)+2f(z), which were introduced and investigated by Baak (2006). The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias' stability theorem that appeared in his paper (1978)

Cauchy-Jensen additive mappings in quasi-Banach algebras and its applications

In this paper, we prove the Hyers-Ulam stability of homomorphisms in quasi-Banach algebras and of generalized derivations on quasi-Banach algebras for the following Cauchy-Jensen additive mapping

Controlled finite continuous frames

In this paper, we present controlled finite continuous frames in a finite dimensional Hilbert space and we study some properties of them. Parseval controlled integral frames are presented and we characterize operators that construct controlled integral finite frames