Stability of functional equations on hypergroups (Q5964962)

Suppose that \(K\) is a locally compact hypergroup and \(f, g, h, k, l:K\to \mathbb{C}\) are continuous functions. In this paper, the author proves a Hyers-Ulam-type stability problem for the functional equations \(f(x*y)=g(x)h(y)+k(y)\) and \(f(x*y)=g(x)h(y)+k(x)+l(y)\) \((x, y\in K)\) generalizing the superstability of exponential functions and the stability of additive functions.