Abstract
We prove new results on Ulam stability of the nonhomogeneous Cauchy functional equation f (x + y) = f (x) f (y) + d(x, y) in the class of mappings f from a square symmetric groupoid (H, +) into the set of reals . The mapping d : H-2 -> R is assumed to be given and satisfy some weak natural assumption. The equation arises naturally, e.g., in the theory of information in a description of generating functions of branching measures of information. Moreover, we provide a suitable example of application of our results in this area at the very end of this paper. The main tool used in the proofs is the Banach limit.