On strong summability of sequences

Abstract

 We extend the notion of strong summability of sequences by matrix methods. Combining the notions of strong summability given by D. Borwein and I. J. Maddox we come to a more general notion. The properties of the extended strong summability are characterized and relations between strong and ordinary summabilities are described. The defined notion of strong summability is applied to certain families of summability methods, including some families of generalized Nörlund methods. Partial cases are the families of Cesàro and Euler-Knopp methods.