An existence and stability theorem for a class of functional equations.
Consider the class of functional equationsg[F(x,y)] = H[g(x),g(y)],where g: E --> X, f: E x E --> E, H: X x X --> X, E is a set and (X,d) is a complete metric space. In this paper we prove that, under suitable hypotheses on F, H and ∂(x,y), the existence of a solution of the functional inequalityd(f[F(x,y)],H[f(x),f(y)]) ≤ ∂(x,y),implies the existence of a solution of the above equation.