International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 2, Pages 297-299

Divergent sequences satisfying the linear fractional transformations

A. McD. Mercer

Department of Mathematics and Statistics, University of Guelph, Ontario, N1G 2W1, Canada

Received 26 August 1991; Revised 31 March 1992

Copyright © 1993 A. McD. Mercer. 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.


A real sequence {xn}1 which satisfies the recurrence xn+1=axn+bcxn+d, in which all of a,b,c,d are real will, for certain values of these constants, be divergent. It is the purpose of this note to examine the limit limN1Nn=1Nf(xn):fC(,) in these cases. Except for certain exceptional values of a,b,c,d this value is found for almost all x1.