Abstract

The well-known summability methods of Euler and Borel are studied as mappings from 1 into 1. In this setting, the following Tauberian results are proved: if x is a sequence that is mapped into 1 by the Euler-Knopp method Er with r>0 (or the Borel matrix method) and x satisfies n=0|xnxn+1|n<, then x itself is in 1.