Asymptotic equivalence and summability

Abstract

This paper is a study of the relatioship. between the asymptotic equivalence of two sequences (limnxn/yn=1) and three variatious of this equivalence for a sequence-to-sequence transformation A, the three variations are give by the ratios RmAx/RmAy. SmAx/SmAy, And μmAx/μmAy, where RmAz:=∑n≥m|(Az)n|, SmAz:=∑n≤m|(Az)n|, and μmAz:=supn≥m|(Az)n|.

Keywords

• asymptotically regular
• asymptotic equivalence
• Nörland-type matrix N¯p.