Additive $f$-bimorphisms and Cosine Type Equations


C.-S. Lin, Y.J. Cho


We introduce the notion of an additive $f$-bimorphism, and study the relationship between the cosine functional equation and the additive $f$-bimorphism. Indeed, the former may be characterized in terms of the latter. Moreover, some generalized cosine functional equations are presented, which may be similarly characterized.