A limit theorem for triangle functions

A wide class of triangle functions that can be interpreted as generalized pseudo-convolutions of distribution functions has been considered. In order to find out whether a nontrivial limit for the sequence of the pseudo-convolutions of distribution functions exists or not, some pseudo-Laplace-type transformations have been introduced. The main result is illustrated with a family of pseudo-convolutions based on a family of Schweizer–Sklar t-norms and another example is given with a calculation of the analytical form of the limit function