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International Journal of Mathematics and Mathematical Sciences
Volume 28, Issue 2, Pages 103-109
http://dx.doi.org/10.1155/S0161171201006512

The Abel-type transformations into Gw

Savannah State University, Savannah, GA 31404, USA

Received 16 January 2001

Copyright © 2001 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

The Abel-type matrix Aα,t was introduced and studied as a mapping into by Lemma (1999). The purpose of this paper is to study these transformations as mappings into Gw. The necessary and sufficient conditions for Aα,t to be Gw-Gw are established. The strength of Aα,t in the Gw-Gw setting is investigated. Also, it is shown that Aα,t is translative in the Gw-Gw senses for certain sequences.