In [32] we presented an overview of concepts, facts and results on triangle functions based on the notions of t-norm, copula, (generalized) convolution, semicopula, quasi-copula. Here, we continue our presentation. In particular, we treat the concept of duality and study a few important cases of functional equations and inequalities for triangle functions like, e.g., convolution, Cauchy's equation, dominance, and Jensen convexity
