International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 10, Pages 637-643
doi:10.1155/S0161171202005331
Rate preservation of double sequences under l-l type transformation
Department of Mathematics and Statistics, University of North Florida, Building 11, Jacksonville 32224, FL, USA
Received 30 May 2000
Copyright © 2002 Richard F. Patterson. 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
Following the concepts of divergent rate preservation for ordinary sequences, we present a notion of rates preservation of divergent double sequences under l-l type transformations. Definitions for Pringsheim limit inferior and superior are also presented. These definitions and the notion of asymptotically equivalent double sequences, are used to present necessary and sufficient conditions on the entries of a four-dimensional matrix such that, the rate of divergence is preserved for a given double sequences under l-l type mapping where l=:{xk,l:∑k,l=1,1∞,∞|xk,l|<∞}.