On a generalized Hyers-Ulam stability of trigonometric functional equations (Q442979)

Summary: Let \(G\) be an abelian group, let \(\mathbb C\) be the field of complex numbers, and let \(f, g : G \rightarrow \mathbb C\). We consider the generalized Hyers-Ulam stability for a class of trigonometric functional inequalities, \[ |f(x - y) - f(x)g(y) + g(x)f(y)| \leq \psi(y), |g(x - y) - g(x)g(y) - f(x)f(y)| \leq \psi(y), \] where \(\psi : G \rightarrow \mathbb R\) is an arbitrary nonnegative function.