International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 4, Pages 755-762
doi:10.1155/S0161171293000948

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|.