On the stability of a class of Cosine type functional equations

The aim of this paper is to investigate the stability problem for the pexiderized trigonometric functional equation f1(xy) + f2(xσ(y)) = 2g1(x)g2(y), x, y ∈ G, (E) where G is an arbitrary group, f1, f2, g1and g2 are complex valued functions on G and σ is an involution of G. Results of this paper also can be extended to the setting of monoids (that is, a semigroup with identity) that need not be abelian. © Soc. Paran. de Mat