Abstract

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.