On a Generalized Hyers-Ulam Stability of Trigonometric Functional Equations

[摘要] LetGbe an Abelian group, letℂbe the field of complex numbers, and letf,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), whereψ:G→ℝis an arbitrary nonnegative function.

[学科分类] 应用数学