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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Wiley
1993-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171293000353 |
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| _version_ | 1832560610567520256 |
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| author | A. McD. Mercer |
| author_facet | A. McD. Mercer |
| author_sort | A. McD. Mercer |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-9556465cdad4487b9c583befa0a069af |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1993-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-9556465cdad4487b9c583befa0a069af2025-02-03T01:27:10ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251993-01-0116229729910.1155/S0161171293000353Divergent sequences satisfying the linear fractional transformationsA. McD. Mercer0Department of Mathematics and Statistics, University of Guelph, Ontario, N1G 2W1, CanadaA 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.http://dx.doi.org/10.1155/S0161171293000353divergent serieslinear fractional transformationsergodic theoryCesaro means. |
| spellingShingle | A. McD. Mercer Divergent sequences satisfying the linear fractional transformations International Journal of Mathematics and Mathematical Sciences divergent series linear fractional transformations ergodic theory Cesaro means. |
| title | Divergent sequences satisfying the linear fractional transformations |
| title_full | Divergent sequences satisfying the linear fractional transformations |
| title_fullStr | Divergent sequences satisfying the linear fractional transformations |
| title_full_unstemmed | Divergent sequences satisfying the linear fractional transformations |
| title_short | Divergent sequences satisfying the linear fractional transformations |
| title_sort | divergent sequences satisfying the linear fractional transformations |
| topic | divergent series linear fractional transformations ergodic theory Cesaro means. |
| url | http://dx.doi.org/10.1155/S0161171293000353 |
| work_keys_str_mv | AT amcdmercer divergentsequencessatisfyingthelinearfractionaltransformations |