Year: 2026
Type: article
Abstract: In this paper, we investigate the stability and superstability of a specific class of functional inequalities associated with centrally extended ∗-derivations on Banach ∗-algebras. A CE ∗-derivation δ:R→R is defined as an additive mapping satisfying δ(x+y)−δ(x)−δ(y)∈Z(R) and δ(xy)−δ(x)y∗−xδ(y)∈Z(R) for all x,y∈R, where Z(R) denotes the center of the ring. We consider the functional inequality ∥[a1δ(x1)+a2δ(x2)+a3δ(x3),w]∥ ≤ ∥[δ(a1x1+a2x2+a3x3),w]∥ + Φ(x1,x2,x3,w), where Φ is a perturbing term. By employing the direct method, we establish several theorems concerning the Hyers–Ulam stability of this inequality in the context of unital Banach ∗-algebras. Furthermore, we provide sufficient conditions under which these functional inequalities exhibit superstability. We also explore the implications of our results for linear ∗-derivations in semiprime Banach ∗-algebras with no nonzero central ideals.
Source: Mathematics
DOI: 10.3390/math14091407
Authors: Ick-Soon Chang, Jaiok Roh
Institutions: Chungnam National University, Hallym University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
Award: G4261466849
OpenAlex ID: W7155162472