International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 2, Pages 297-299
doi:10.1155/S0161171293000353

Divergent sequences satisfying the linear fractional transformations

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 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.