On the stability of some functional equations for generalized hyperbolic functions and for the generalized cosine equation (Q1895191)

The authors prove some stability results (in the sense of Hyers-Ulam) concerning some systems of functional equations for generalized hyperbolic functions. Moreover they prove a generalization of a result of \textit{J. A. Baker} [Proc. Am. Math. Soc. 80, 411-416 (1980; Zbl 0448.39003)] on the superstability of the cosine functional equation. It has to be noted that the present result is proved without making use of the knowledge of the solutions of the generalized cosine functional equations.