Rainwater-Simons-type convergence theorems for generalized convergence methods

摘要

We extend the well-known Rainwater-Simons convergence theorem to variousgeneralized convergence methods such as strong matrix summability, statisticalconvergence and almost convergence. In fact we prove these theorems not onlyfor boundaries but for the more general notion of (I)-generating setsintroduced by Fonf and Lindenstrauss.