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Year 2018, Volume: 6 Issue: 2, 177 - 192, 24.12.2018

Abstract

References

  • [1] Amleh A. M., Grove E. A., Ladas G., Georgiou D. A., On the recursive sequence , J. Math. Anal. Appl., 233, no. 2, (1999),790-798.
  • [2] Cinar C., On the positive solutions of the difference equation , Appl. Math. Comp., 158 (3), (2004), 809–812.
  • [3] Cinar C., On the positive solutions of the difference equation , Appl. Math. Comp., 158 (3), (2004), 793–797.
  • [4] Cinar C., On the positive solutions of the difference equation, Appl. Math. Comp., 156 (3), (2004), 587–590.
  • [5] Elabbasy E. M., El-Metwally H., Elsayed E. M., On the difference equation , Advances in Difference Equation, (2006), 1-10.
  • [6] Elabbasy E. M., El-Metwally H., Elsayed E. M., Qualitative behavior of higher order difference equation, Soochow Journal of Mathematics, 33(4), (2007), 861-873.
  • [7] Elabbasy E. M., El-Metwally H., Elsayed E. M., Global attractivity and periodic character of a fractional difference equation of order three, Yokohama Mathematical Journal, 53, (2007), 89-100.
  • [8] Elabbasy E. M., El-Metwally H., Elsayed E. M., On the difference equation , J. Conc. Appl. Math., 5(2), (2007), 101-113.
  • [9] Elabbasy E. M. and Elsayed E. M., On the Global Attractivity of Difference Equation of Higher Order, Carpathian Journal of Mathematics, 24 (2), (2008), 45–53.
  • [10] Elsayed E. M., On the Solution of Recursive Sequence of Order Two, Fasciculi Mathematici, 40, (2008), 5–13.
  • [11] Elsayed E. M., Dynamics of a Recursive Sequence of Higher Order, Communications on Applied Nonlinear Analysis, 16 (2), (2009), 37–50.
  • [12] Elsayed E. M., Solution and atractivity for a rational recursive sequence, Discrete Dynamics in Nature and Society, (2011), 17.
  • [13] Elsayed E. M., On the solution of some difference equation, Europan Journal of Pure and Applied Mathematics, 4 (3), (2011), 287–303.
  • [14] Elsayed E. M., On the Dynamics of a higher order rational recursive sequence, Communications in Mathematical Analysis, 12 (1), (2012), 117–133.
  • [15] Elsayed E. M., Solution of rational difference system of order two, Mathematical and Computer Modelling, 55, (2012), 378–384.
  • [16] Gibbons C. H., Kulenović M. R. S. and Ladas G., On the recursive sequence , Math. Sci. Res. Hot-Line, 4, 2, (2000), 1-11.
  • [17] Kulenović M.R.S., Ladas G., Sizer W.S., On the recursive sequence Math. Sci. Res. Hot-Line, 2, 5, (1998), 1-16.
  • [18] Stevic S., On the recursive sequence , Taiwanese J. Math., 6, 3, (2002), 405-414.
  • [19] Şimşek D., Çınar C. and Yalçınkaya İ., On the recursive sequence , Int. J. Contemp. Math. Sci., 1, 9-12, (2006), 475-480.
  • [20] Şimşek D., Çınar C., Karataş R., Yalçınkaya İ., On the recursive sequence , Int. J. Pure Appl. Math., 27, 4, (2006), 501-507.
  • [21] Şimşek D., Çınar C., Karataş R., Yalçınkaya İ., "n the recursive sequence , Int. J. Pure Appl. Math., 28, 1, (2006), 117-124.
  • [22] Şimşek D., Çınar C., Yalçınkaya İ., On The Recursive Sequence x(n+1) = x[n-(5k+9)] / 1+x(n-4)x(n-9) x[n-(5k+4)], Taiwanese Journal of Mathematics, Vol. 12, 5, (2008), 1087-1098.
  • [23] Şimşek D., Doğan A., On A Class of Recursive Sequence, Manas Journal of Engineering, 2, 1, (2014), 16-22.
  • [24] Şimşek D., Eröz M., Solutions of The Rational Difference Equations , Manas Journal of Engineering, 4, 1, (2016), 12-20.

Solutions of the Rational Difference Equations

Year 2018, Volume: 6 Issue: 2, 177 - 192, 24.12.2018

Abstract

In
this paper the solutions of the following difference equation is examined,






(1)






where
the initial conditions are positive real numbers.

References

  • [1] Amleh A. M., Grove E. A., Ladas G., Georgiou D. A., On the recursive sequence , J. Math. Anal. Appl., 233, no. 2, (1999),790-798.
  • [2] Cinar C., On the positive solutions of the difference equation , Appl. Math. Comp., 158 (3), (2004), 809–812.
  • [3] Cinar C., On the positive solutions of the difference equation , Appl. Math. Comp., 158 (3), (2004), 793–797.
  • [4] Cinar C., On the positive solutions of the difference equation, Appl. Math. Comp., 156 (3), (2004), 587–590.
  • [5] Elabbasy E. M., El-Metwally H., Elsayed E. M., On the difference equation , Advances in Difference Equation, (2006), 1-10.
  • [6] Elabbasy E. M., El-Metwally H., Elsayed E. M., Qualitative behavior of higher order difference equation, Soochow Journal of Mathematics, 33(4), (2007), 861-873.
  • [7] Elabbasy E. M., El-Metwally H., Elsayed E. M., Global attractivity and periodic character of a fractional difference equation of order three, Yokohama Mathematical Journal, 53, (2007), 89-100.
  • [8] Elabbasy E. M., El-Metwally H., Elsayed E. M., On the difference equation , J. Conc. Appl. Math., 5(2), (2007), 101-113.
  • [9] Elabbasy E. M. and Elsayed E. M., On the Global Attractivity of Difference Equation of Higher Order, Carpathian Journal of Mathematics, 24 (2), (2008), 45–53.
  • [10] Elsayed E. M., On the Solution of Recursive Sequence of Order Two, Fasciculi Mathematici, 40, (2008), 5–13.
  • [11] Elsayed E. M., Dynamics of a Recursive Sequence of Higher Order, Communications on Applied Nonlinear Analysis, 16 (2), (2009), 37–50.
  • [12] Elsayed E. M., Solution and atractivity for a rational recursive sequence, Discrete Dynamics in Nature and Society, (2011), 17.
  • [13] Elsayed E. M., On the solution of some difference equation, Europan Journal of Pure and Applied Mathematics, 4 (3), (2011), 287–303.
  • [14] Elsayed E. M., On the Dynamics of a higher order rational recursive sequence, Communications in Mathematical Analysis, 12 (1), (2012), 117–133.
  • [15] Elsayed E. M., Solution of rational difference system of order two, Mathematical and Computer Modelling, 55, (2012), 378–384.
  • [16] Gibbons C. H., Kulenović M. R. S. and Ladas G., On the recursive sequence , Math. Sci. Res. Hot-Line, 4, 2, (2000), 1-11.
  • [17] Kulenović M.R.S., Ladas G., Sizer W.S., On the recursive sequence Math. Sci. Res. Hot-Line, 2, 5, (1998), 1-16.
  • [18] Stevic S., On the recursive sequence , Taiwanese J. Math., 6, 3, (2002), 405-414.
  • [19] Şimşek D., Çınar C. and Yalçınkaya İ., On the recursive sequence , Int. J. Contemp. Math. Sci., 1, 9-12, (2006), 475-480.
  • [20] Şimşek D., Çınar C., Karataş R., Yalçınkaya İ., On the recursive sequence , Int. J. Pure Appl. Math., 27, 4, (2006), 501-507.
  • [21] Şimşek D., Çınar C., Karataş R., Yalçınkaya İ., "n the recursive sequence , Int. J. Pure Appl. Math., 28, 1, (2006), 117-124.
  • [22] Şimşek D., Çınar C., Yalçınkaya İ., On The Recursive Sequence x(n+1) = x[n-(5k+9)] / 1+x(n-4)x(n-9) x[n-(5k+4)], Taiwanese Journal of Mathematics, Vol. 12, 5, (2008), 1087-1098.
  • [23] Şimşek D., Doğan A., On A Class of Recursive Sequence, Manas Journal of Engineering, 2, 1, (2014), 16-22.
  • [24] Şimşek D., Eröz M., Solutions of The Rational Difference Equations , Manas Journal of Engineering, 4, 1, (2016), 12-20.
There are 24 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Dagıstan Şimşek This is me

Peil Esengul Kyzy 0000-0003-1083-4191

Publication Date December 24, 2018
Published in Issue Year 2018 Volume: 6 Issue: 2

Cite

APA Şimşek, D., & Esengul Kyzy, P. (2018). Solutions of the Rational Difference Equations. MANAS Journal of Engineering, 6(2), 177-192.
AMA Şimşek D, Esengul Kyzy P. Solutions of the Rational Difference Equations. MJEN. December 2018;6(2):177-192.
Chicago Şimşek, Dagıstan, and Peil Esengul Kyzy. “Solutions of the Rational Difference Equations”. MANAS Journal of Engineering 6, no. 2 (December 2018): 177-92.
EndNote Şimşek D, Esengul Kyzy P (December 1, 2018) Solutions of the Rational Difference Equations. MANAS Journal of Engineering 6 2 177–192.
IEEE D. Şimşek and P. Esengul Kyzy, “Solutions of the Rational Difference Equations”, MJEN, vol. 6, no. 2, pp. 177–192, 2018.
ISNAD Şimşek, Dagıstan - Esengul Kyzy, Peil. “Solutions of the Rational Difference Equations”. MANAS Journal of Engineering 6/2 (December 2018), 177-192.
JAMA Şimşek D, Esengul Kyzy P. Solutions of the Rational Difference Equations. MJEN. 2018;6:177–192.
MLA Şimşek, Dagıstan and Peil Esengul Kyzy. “Solutions of the Rational Difference Equations”. MANAS Journal of Engineering, vol. 6, no. 2, 2018, pp. 177-92.
Vancouver Şimşek D, Esengul Kyzy P. Solutions of the Rational Difference Equations. MJEN. 2018;6(2):177-92.

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