On the Superstability of Trigonometric Type Functional Equations

The aim of this paper is to study the superstability for the mixed trigonometric functional equation: ,,),()(2))(()(Gyxygxfyxfxyf∈=−σ)(,gfEand the stability of the Pexider type functional equation: ,,),()(2))(()(Gyxyhxgyxfxyf∈=−σ)(,,hgfEwhere G is any group, not necessarily abelian, gf,and h are unknown complex valued functions and σ is an involution of G. As a consequence we prove that if fsatisfies the inequality δσ≤−−)()(2))(()(yfxfyxfxyf for all Gyx∈,then fis bounded.