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International Journal of Mathematics and Mathematical Sciences
Volume 16, Issue 4, Pages 755-762
http://dx.doi.org/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 Hindawi Publishing Corporation. 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:=nm|(Az)n|, SmAz:=nm|(Az)n|, and μmAz:=supnm|(Az)n|.