Divergent sequences satisfying the linear fractional transformations
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 o...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
1993-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171293000353 |
| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |