Rainwater-Simons-type convergence theorems for generalized convergence methods

Details Rainwater-Simons-type convergence theorems for generalized convergence methods Rainwater-Simons-type convergence theorems for generalized convergence methods

2010-11-10

arxiv.org/abs/1011.2365v2

Mathematics

Functional Analysis

10 pages, version 2, references added, one remark added, revised version accepted for publication in Acta et Commentationes Un

Scientific paper

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.

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