On the Butler–Rassias Functional Equation and its Generalized Hyers–Ulam Stability

In this paper, we present a recent development of the Hyers–Ulam stability of the Butler–Rassias functional equation \(f(x + y) - f(x)f(y) = d\sin x\sin y\). We also show our most recent results on a Butler–Rassias type functional equation with complex variables.