On a Generalized Hyers-Ulam Stability of Trigonometric Functional Equations

Abstract

Let $G$ be an Abelian group, let $ℂ$ be the field of complex numbers, and let $f,g:G\to ℂ$. We consider the generalized Hyers-Ulam stability for a class of trigonometric functional inequalities, $\left|f\right(x-y)-f(x\left)g\right(y)+g(x\left)f\right(y\left)\right|\le \psi \left(y\right),\left|g\right(x-y)-g(x\left)g\right(y)-f(x\left)f\right(y\left)\right|\le \psi \left(y\right)$, where $\psi :G\to ℝ$ is an arbitrary nonnegative function.