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Solutions Of The Rational Difference Equations X(n 1)=x(n (2k 1)) /1 X(n-k)

Year 2017, Volume: 5 Issue: 3, 57 - 68, 01.12.2017

Abstract

In this paper the solutions of the following difference equation is examined, x(n 1)=x(n (2k 1)) /1 x(n-k) (1)where the initial conditions are positive real numbers.

References

  • [1] Amleh A. M., Grove E. A., Ladas G. and Georgiou D. A., On the recursive sequence , J. Math. Anal. Appl., 233, no. 2, 790-798, 1999.
  • [2] Cinar C., On the positive solutions of the difference equation , Appl. Math.
  • Comp., 158 (3), 809–812, 2004.
  • [3] Cinar C., On the positive solutions of the difference equation , Appl. Math. Comp., 158 (3), 793–797, 2004.
  • [4] Cinar C., On the positive solutions of the difference equation , Appl. Math. Comp., 156 (3), 587–590, 2004.
  • [5] Elabbasy E. M., El-Metwally H. and Elsayed E. M., On the difference equation , Advances in Difference Equation, Volume 2006,Article ID 82579, 1-10, 2006.
  • [6] Elabbasy E. M., El-Metwally H. and Elsayed E. M., Qualitative behavior of higher order difference equation, Soochow Journal of Mathematics, 33(4), 861-873, 2007.
  • [7] Elabbasy E. M., El-Metwally H. and Elsayed E. M., Global attractivity and periodic character of a fractional difference equation of order three, Yokohama Mathematical Journal, 53, 89-100, 2007.
  • [8] Elabbasy E. M., El-Metwally H. and Elsayed E. M., On the difference equation , J. Conc. Appl. Math., 5(2), 101-113, 2007.
  • [9] Elabbasy E. M. and Elsayed E. M., On the Global Attractivity of Difference Equation of Higher
  • Order, Carpathian Journal of Mathematics, 24 (2), 45–53, 2008.
  • [10] Elsayed E. M., On the Solution of Recursive Sequence of Order Two, Fasciculi Mathematici, 40, 5–13, 2008.
  • [11] Elsayed E. M., Dynamics of a Recursive Sequence of Higher Order, Communications on Applied Nonlinear Analysis, 16 (2), 37–50, 2009.
  • [12] Elsayed E. M., Solution and atractivity for a rational recursive sequence, Discrete Dynamics in Nature and Society, Volume 2011, Article ID 982309, 17 pages, 2011.
  • [13] Elsayed E. M., On the solution of some difference equation, Europan Journal of Pure and Applied
  • Mathematics, 4 (3), 287–303, 2011.
  • [14] Elsayed E. M., On the Dynamics of a higher order rational recursive sequence, Communications in
  • Mathematical Analysis, 12 (1), 117–133, 2012.
  • [15] Elsayed E. M., Solution of rational difference system of order two, Mathematical and Computer Modelling, 55, 378–384, 2012.
  • [16] Gibbons C. H., Kulenović M. R. S. and Ladas G., On the recursive sequence , Math. Sci. Res. Hot-Line, 4, no. 2, 1-11, 2000.
  • [17] Kulenović M.R.S., Ladas G. and Sizer W.S., On the recursive sequence Math. Sci. Res. Hot-Line, Vol. 2, No. 5, 1-16, 1998.
  • [18] Stevic S. , On the recursive sequence , Taiwanese J. Math., Vol.6, No. 3, 405-414
  • 2002.
  • [19] Şimşek D., Çınar C. and Yalçınkaya İ., On the recursive sequence , Int. J. Contemp. Math. Sci., 1, no. 9-12, 475-480, 2006.
  • [20] Şimşek D., Çınar C., Karataş R. and Yalçınkaya İ., On the recursive sequence , Int. J. Pure Appl. Math., 27, no. 4, 501-507, 2006.
  • [21] Şimşek D., Çınar C., Karataş R. and Yalçınkaya İ.

Rasyonel Fark Denkleminin Çözümleri

Year 2017, Volume: 5 Issue: 3, 57 - 68, 01.12.2017

Abstract

Aşağıdaki Rasyonel fark denkleminin çözümlerini incelendi

References

  • [1] Amleh A. M., Grove E. A., Ladas G. and Georgiou D. A., On the recursive sequence , J. Math. Anal. Appl., 233, no. 2, 790-798, 1999.
  • [2] Cinar C., On the positive solutions of the difference equation , Appl. Math.
  • Comp., 158 (3), 809–812, 2004.
  • [3] Cinar C., On the positive solutions of the difference equation , Appl. Math. Comp., 158 (3), 793–797, 2004.
  • [4] Cinar C., On the positive solutions of the difference equation , Appl. Math. Comp., 156 (3), 587–590, 2004.
  • [5] Elabbasy E. M., El-Metwally H. and Elsayed E. M., On the difference equation , Advances in Difference Equation, Volume 2006,Article ID 82579, 1-10, 2006.
  • [6] Elabbasy E. M., El-Metwally H. and Elsayed E. M., Qualitative behavior of higher order difference equation, Soochow Journal of Mathematics, 33(4), 861-873, 2007.
  • [7] Elabbasy E. M., El-Metwally H. and Elsayed E. M., Global attractivity and periodic character of a fractional difference equation of order three, Yokohama Mathematical Journal, 53, 89-100, 2007.
  • [8] Elabbasy E. M., El-Metwally H. and Elsayed E. M., On the difference equation , J. Conc. Appl. Math., 5(2), 101-113, 2007.
  • [9] Elabbasy E. M. and Elsayed E. M., On the Global Attractivity of Difference Equation of Higher
  • Order, Carpathian Journal of Mathematics, 24 (2), 45–53, 2008.
  • [10] Elsayed E. M., On the Solution of Recursive Sequence of Order Two, Fasciculi Mathematici, 40, 5–13, 2008.
  • [11] Elsayed E. M., Dynamics of a Recursive Sequence of Higher Order, Communications on Applied Nonlinear Analysis, 16 (2), 37–50, 2009.
  • [12] Elsayed E. M., Solution and atractivity for a rational recursive sequence, Discrete Dynamics in Nature and Society, Volume 2011, Article ID 982309, 17 pages, 2011.
  • [13] Elsayed E. M., On the solution of some difference equation, Europan Journal of Pure and Applied
  • Mathematics, 4 (3), 287–303, 2011.
  • [14] Elsayed E. M., On the Dynamics of a higher order rational recursive sequence, Communications in
  • Mathematical Analysis, 12 (1), 117–133, 2012.
  • [15] Elsayed E. M., Solution of rational difference system of order two, Mathematical and Computer Modelling, 55, 378–384, 2012.
  • [16] Gibbons C. H., Kulenović M. R. S. and Ladas G., On the recursive sequence , Math. Sci. Res. Hot-Line, 4, no. 2, 1-11, 2000.
  • [17] Kulenović M.R.S., Ladas G. and Sizer W.S., On the recursive sequence Math. Sci. Res. Hot-Line, Vol. 2, No. 5, 1-16, 1998.
  • [18] Stevic S. , On the recursive sequence , Taiwanese J. Math., Vol.6, No. 3, 405-414
  • 2002.
  • [19] Şimşek D., Çınar C. and Yalçınkaya İ., On the recursive sequence , Int. J. Contemp. Math. Sci., 1, no. 9-12, 475-480, 2006.
  • [20] Şimşek D., Çınar C., Karataş R. and Yalçınkaya İ., On the recursive sequence , Int. J. Pure Appl. Math., 27, no. 4, 501-507, 2006.
  • [21] Şimşek D., Çınar C., Karataş R. and Yalçınkaya İ.
There are 26 citations in total.

Details

Other ID JA84NZ92DP
Journal Section Research Article
Authors

D. Şimşek This is me

B. Oğul This is me

Publication Date December 1, 2017
Published in Issue Year 2017 Volume: 5 Issue: 3

Cite

APA Şimşek, D., & Oğul, B. (2017). Solutions Of The Rational Difference Equations X(n 1)=x(n (2k 1)) /1 X(n-k). MANAS Journal of Engineering, 5(3), 57-68.
AMA Şimşek D, Oğul B. Solutions Of The Rational Difference Equations X(n 1)=x(n (2k 1)) /1 X(n-k). MJEN. December 2017;5(3):57-68.
Chicago Şimşek, D., and B. Oğul. “Solutions Of The Rational Difference Equations X(n 1)=x(n (2k 1)) /1 X(n-K)”. MANAS Journal of Engineering 5, no. 3 (December 2017): 57-68.
EndNote Şimşek D, Oğul B (December 1, 2017) Solutions Of The Rational Difference Equations X(n 1)=x(n (2k 1) /1 X(n-k). MANAS Journal of Engineering 5 3 57–68.
IEEE D. Şimşek and B. Oğul, “Solutions Of The Rational Difference Equations X(n 1)=x(n (2k 1)) /1 X(n-k)”, MJEN, vol. 5, no. 3, pp. 57–68, 2017.
ISNAD Şimşek, D. - Oğul, B. “Solutions Of The Rational Difference Equations X(n 1)=x(n (2k 1)) /1 X(n-K)”. MANAS Journal of Engineering 5/3 (December 2017), 57-68.
JAMA Şimşek D, Oğul B. Solutions Of The Rational Difference Equations X(n 1)=x(n (2k 1)) /1 X(n-k). MJEN. 2017;5:57–68.
MLA Şimşek, D. and B. Oğul. “Solutions Of The Rational Difference Equations X(n 1)=x(n (2k 1)) /1 X(n-K)”. MANAS Journal of Engineering, vol. 5, no. 3, 2017, pp. 57-68.
Vancouver Şimşek D, Oğul B. Solutions Of The Rational Difference Equations X(n 1)=x(n (2k 1)) /1 X(n-k). MJEN. 2017;5(3):57-68.

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