International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 4, Pages 749-757

Asymptotic equivalence of sequences and summability

Jinlu Li

Department of Mathematics, Shawnee State University, Portsmouth 45662, OH, USA

Received 14 August 1995; Revised 5 July 1996

Copyright © 1997 Jinlu Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For a sequence-to-sequence transformation A, let RmAx=nm|(Ax)n| and μmAx=supnm|(Ax)n|. The purpose of this paper is to study the relationship between the asymptotic equivalence of two sequences (limnxn/yn=1) and the variations of asymptotic equivalence based on the ratios RmAx/RmAy and μmAx/μmAy.