On the superstability of the pexider type generalized trigonometric functional equations

The aim of this paper is to investigate the superstability problem for the pexiderized trigonometric functional equation ∑ϕ∈Φ∫Kf(xkϕ(y)k-1)duK(k) = |Φ|g(x)h(y), x,y ∈ G,where G is any topological group, K is a compact subgroup of G, ωK is the normalized Haar measure of K, Φ is a finite group of K-invariant morphisms of G and f,g,h are continuous complex-valued functions.Consequently, we have generalized the results of stability for d'Alembert's and Wilson's equations by R. Badora, J. Baker, B. Bouikhalene, P. Gavruta, S. Kabbaj, Pl. Kannappan, G. H. Kim, J.M. Rassias, A. Roukbi, L. Székelyhidi, D. Zeglami, etc.