Hyers–Ulam stability of generalized Wilson’s and d’Alembert’s functional equations

We study the Hyers–Ulam stability problem for the generalized Wilson’s equation (Formula presented.) where G is an arbitrary locally compact group, not necessarily abelian, 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: G ⟶ C are continuous complex-valued functions. We dont impose that f satisfies the Kannappan type condition. In addition, superstability problem for some related functional equations are considered. © 2013, African Mathematical Union and Springer-Verlag Berlin Heidelberg.