Divergent sequences satisfying the linear fractional transformations - A. McD. Mercer (International Journal of Mathematics and Mathematical Sciences)
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 limN→∞1N∑n=1Nf(xn):f∈C(−∞,∞) in these cases. Except for certain exceptional values of a,b,c,d this value is found for almost all x1.