Divergent sequences satisfying the linear fractional transformations

A. McD. Mercer
1993 International Journal of Mathematics and Mathematical Sciences  
A real sequence{xn}1∞which satisfies the recurrencexn+1=axn+bcxn+d, in which all ofa,b,c,dare real will, for certain values of these constants, be divergent. It is the purpose of this note to examine the limitlimN→∞1N∑n=1Nf(xn):f∈C(−∞,∞)in these cases. Except for certain exceptional values ofa,b,c,dthis value is found for almost allx1.
doi:10.1155/s0161171293000353 fatcat:nvjpag7envcv3j5z6eci4rhwxi