Sharp boundedness conditions for a difference equation via the Chebyshev polynomials
| dc.contributor.author | Karakostas, G. L. | en |
| dc.contributor.author | Mansour, T. | en |
| dc.date.accessioned | 2015-11-24T17:27:58Z | |
| dc.date.available | 2015-11-24T17:27:58Z | |
| dc.identifier.issn | 1023-6198 | - |
| dc.identifier.uri | https://olympias.lib.uoi.gr/jspui/handle/123456789/13480 | |
| dc.rights | Default Licence | - |
| dc.subject | difference equations | en |
| dc.subject | chebyshev polynomials | en |
| dc.subject | positive solution | en |
| dc.subject | boundedness | en |
| dc.subject | global attractivity | en |
| dc.title | Sharp boundedness conditions for a difference equation via the Chebyshev polynomials | en |
| heal.abstract | Sufficient conditions are provided for the boundedness of all positive solutions of the nonlinear difference equation x(n+1)=x(n)(gamma) f(x(n-k)), where gamma>0 and f : [0, +infinity)-->[0, +infinity) is a given function. In case k=1 the classical Chebyshev polynomials of the second kind are used to obtain such sharp sufficient conditions. Also some convergence results are given. The results extend those given in [E. Camuzis, G. Ladas, I.W. Rodrigues and S. Northshield, The rational recursive sequence x(n+1)=(betax(n)(2))/(1+x(n-1)(2)), Advances in difference equations, Comp. Math. Appl. 28 (1994), 37-43; E. Camuzis, E.A. Grove, G. Ladas and V.L. Kosic, Monotone unstable solutions of difference equations and conditions for boundedness, J. Differ Equations Appl. 1 (1995), 17-44; George L. Karakostas, Asymptotic behavior of the solutions of the difference equation x(n+1)= x(n)(2)f(x(n-1)), J. Differ. Equations Appl. 9(6) (2001), 599-602; V.L. Kocic and G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order and Applications, Kluwer Academic Publishers, Dordrecht, 1993; Wan-Tong Li, Hong-Rui Sun and Xing-Xue Yan, The asymptotic behavior of a higher order delay nonlinear difference equations, Indian J Pure Appl. Math. 34(10) (2003), 1431-1441; D.C. Zhang, B. Shi and M.J. Gai, On the rational recursive sequence x(n+1)= bx(n)(2)/(1+x(n-1)(2)), Indian J. Pure Appl. Math. (2) 32(5) (2001), 657-663] concerning boundedness of the solutions. | en |
| heal.access | campus | - |
| heal.fullTextAvailability | TRUE | - |
| heal.identifier.primary | Doi 10.1080/10236190410001713272 | - |
| heal.identifier.secondary | <Go to ISI>://000223719200002 | - |
| heal.identifier.secondary | http://www.tandfonline.com/doi/pdf/10.1080/10236190410001713272 | - |
| heal.journalName | Journal of Difference Equations and Applications | en |
| heal.journalType | peer reviewed | - |
| heal.language | en | - |
| heal.publicationDate | 2004 | - |
| heal.publisher | Taylor & Francis | en |
| heal.recordProvider | Πανεπιστήμιο Ιωαννίνων. Σχολή Θετικών Επιστημών. Τμήμα Μαθηματικών | el |
| heal.type | journalArticle | - |
| heal.type.el | Άρθρο Περιοδικού | el |
| heal.type.en | Journal article | en |
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