On a Generalized Hyers-Ulam Stability of Trigonometric Functional Equations

Abstract EN

Let G be an Abelian group, let ℂ be the field of complex numbers, and let f,g:G→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)|≤ψ(y), |g(x-y)-g(x)g(y)-f(x)f(y)|≤ψ(y), where ψ:G→ℝ is an arbitrary nonnegative function.