On the Stability of a Class of Functional Equations

In this paper, we study the Baker’s superstability for the following functional equation (E (K)) ∑ φ∈Φ ∫ K f(xkφ(y)k)dωK(k) = |Φ|f(x)f(y), x, y ∈ G where G is a locally compact 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 is a continuous complex-valued function on G satisfying the Kannappan type condition, for all x, y, z ∈ G (*) ∫