International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 4, Pages 755-762
doi:10.1155/S0161171293000948
Asymptotic equivalence and summability
Shawnee State University, 940 2nd Street, Portsmouth 45662, Ohio, USA
Received 6 February 1992; Revised 3 June 1992
Copyright © 1993 Mousa S. Marouf. 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.
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|.