Rainwater-Simons-type convergence theorems for generalized convergence methods

Abstract

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

10 pages, version 2, references added, one remark added, revised version accepted for publication in Acta et Commentationes Universitatis Tartuensis de Mathematica