On the Recursive Sequence ๐ฅ๐+๐=max{๐ฅ๐,๐ด}/๐ฅ๐๐๐ฅ๐โ๐
We investigate the periodic nature of the solution of the max-type difference equation ๐ฅ๐+1=max{๐ฅ๐,๐ด}/๐ฅ2๐๐ฅ๐โ1, ๐=0,1,2,โฆ, where the initial conditions are ๐ฅโ1=๐ด๐1 and ๐ฅ0=๐ด๐2 for ๐ดโ(0,โ), and that ๐1 and ๐2 are positive rational numbers. The results in this paper solve the Open Problem proposed by Gr...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2010/583230 |
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| author | Ibrahim Yalcinkaya Cengiz Cinar Ali Gelisken |
| author_facet | Ibrahim Yalcinkaya Cengiz Cinar Ali Gelisken |
| author_sort | Ibrahim Yalcinkaya |
| collection | DOAJ |
| description | We investigate the periodic nature of the solution of the max-type difference equation ๐ฅ๐+1=max{๐ฅ๐,๐ด}/๐ฅ2๐๐ฅ๐โ1, ๐=0,1,2,โฆ, where the initial conditions are ๐ฅโ1=๐ด๐1 and ๐ฅ0=๐ด๐2 for ๐ดโ(0,โ), and that ๐1 and ๐2 are positive rational numbers. The results in this paper solve the Open Problem proposed by Grove and Ladas (2005). |
| format | Article |
| id | doaj-art-31cec3ee52864aa5826d9bc0f2c894bb |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-31cec3ee52864aa5826d9bc0f2c894bb2025-02-03T06:05:07ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2010-01-01201010.1155/2010/583230583230On the Recursive Sequence ๐ฅ๐+๐=max{๐ฅ๐,๐ด}/๐ฅ๐๐๐ฅ๐โ๐Ibrahim Yalcinkaya0Cengiz Cinar1Ali Gelisken2Mathematics Department, Ahmet Kelesoglu Education Faculty, Selcuk University, Meram Yeni Yol, 42090 Konya, TurkeyMathematics Department, Ahmet Kelesoglu Education Faculty, Selcuk University, Meram Yeni Yol, 42090 Konya, TurkeyMathematics Department, Ahmet Kelesoglu Education Faculty, Selcuk University, Meram Yeni Yol, 42090 Konya, TurkeyWe investigate the periodic nature of the solution of the max-type difference equation ๐ฅ๐+1=max{๐ฅ๐,๐ด}/๐ฅ2๐๐ฅ๐โ1, ๐=0,1,2,โฆ, where the initial conditions are ๐ฅโ1=๐ด๐1 and ๐ฅ0=๐ด๐2 for ๐ดโ(0,โ), and that ๐1 and ๐2 are positive rational numbers. The results in this paper solve the Open Problem proposed by Grove and Ladas (2005).http://dx.doi.org/10.1155/2010/583230 |
| spellingShingle | Ibrahim Yalcinkaya Cengiz Cinar Ali Gelisken On the Recursive Sequence ๐ฅ๐+๐=max{๐ฅ๐,๐ด}/๐ฅ๐๐๐ฅ๐โ๐ Discrete Dynamics in Nature and Society |
| title | On the Recursive Sequence ๐ฅ๐+๐=max{๐ฅ๐,๐ด}/๐ฅ๐๐๐ฅ๐โ๐ |
| title_full | On the Recursive Sequence ๐ฅ๐+๐=max{๐ฅ๐,๐ด}/๐ฅ๐๐๐ฅ๐โ๐ |
| title_fullStr | On the Recursive Sequence ๐ฅ๐+๐=max{๐ฅ๐,๐ด}/๐ฅ๐๐๐ฅ๐โ๐ |
| title_full_unstemmed | On the Recursive Sequence ๐ฅ๐+๐=max{๐ฅ๐,๐ด}/๐ฅ๐๐๐ฅ๐โ๐ |
| title_short | On the Recursive Sequence ๐ฅ๐+๐=max{๐ฅ๐,๐ด}/๐ฅ๐๐๐ฅ๐โ๐ |
| title_sort | on the recursive sequence ๐ฅ๐ ๐ max ๐ฅ๐ ๐ด ๐ฅ๐๐๐ฅ๐ ๐ |
| url | http://dx.doi.org/10.1155/2010/583230 |
| work_keys_str_mv | AT ibrahimyalcinkaya ontherecursivesequencexn1maxxnax2nxn1 AT cengizcinar ontherecursivesequencexn1maxxnax2nxn1 AT aligelisken ontherecursivesequencexn1maxxnax2nxn1 |