Divergent sequences satisfying the linear fractional transformations

A. McD. Mercer

International Journal of Mathematics and Mathematical Sciences, 1993, vol. 16, 1-3

Abstract:

A real sequence { x n } 1 ∞ which satisfies the recurrence x n + 1 = a x n + b c x n + 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 lim N → ∞ 1 N ∑ n = 1 N f ( x n ) : f ∈ C ( − ∞ , ∞ ) in these cases. Except for certain exceptional values of a , b , c , d this value is found for almost all x 1 .

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:653463

DOI: 10.1155/S0161171293000353

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