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Solutions of the System of Maximum Difference Equations

Year 2016, Volume: 4 Issue: 2, 11 - 23, 01.10.2016

Abstract

The behaviour and periodicity of the solutions of the following system of difference equations is
examined

References

  • [1] Amleh A.M. "Boundedness Periodicity and Stability of Some Difference Equations", PhD Thesis, University of Rhode Island, (1998).
  • [2] Çinar C., Stevic S., Yalçınkaya İ "On the positive solutions of reciprocal difference equation with minimum", Journal of Applied Mathematics and Computing, 17, (1-2), (2005), 307-314.
  • [3] Elaydi S."An Introduction to Difference Equations", Spinger-Verlag, New York, (1996).
  • [4] Elsayed E.M., Stevic S."On the max-type equation x_{n+1}=max{A/x_{n},x_{n-2}}", Nonlinear Analysis, TMA 71, (2009), 910-922.
  • [5] Elsayed E.M., Iricanin B., Stevic S. "On the max-type equation x_{n+1} = max{A_{n}/x_{n},x_{n-1}}", ARS Combin., (2010).
  • [6] Feuer J."Periodic solutions of the Lyness max equation", Journal of Mathematical Analysis and Applications, 288, (2003), 147-160.
  • [7] Gelişken A., Çinar C., Karataş R."A note on the periodicity of the Lyness max equation", Advances in Difference Equations, (2008), Article ID 651747, 5.
  • [8] Gelişken A., Çinar C., Yalçınkaya İ. "On the periodicity of a difference equation with maximum", Discrete Dynamics in Nature and Society, (2008), Article ID 820629, 11.
  • [9] Gelişken A., Çinar C., Kurbanlı A.S. "On the asymptotic behavior and periodic nature of a difference equation with maximum", Computers & Mathematics with Applications, 59, (2010), 898-902.
  • [10] Iricanin B., Elsayed, E.M. "On a max-type equation x_{n+1}=max{A/x_{n},x_{n-3}}", Discrete Dynamics in Nature and Society, (2010), Article ID 675413.
  • [11] Kulenevic M.R.S., Ladas G. "Dynamics of Second Order Rational Difference Equations with Open Problems and Conjecture",Boca Raton, London, (2002).
  • [12] Mishev D.P., Patula W.T., Voulov H.D. "A reciprocal difference equation with maximum", Computers & Mathematics with Applications, 43, (2002), 1021-1026.
  • [13] Moybe L.A. "Difference Equations with Public Health Applications", New York, USA, (2000).
  • [14] Огул Б., Шимшек Д." Система решение разностного уравнения", Весник Кыргызского Государственного Технического Университета, N 34, Бишкек, Кыргызстан, (2015).
  • [15] Ogul B., Simsek D. "  Maksimumlu Fark Denklem Sisteminin Çözümleri", Manas Journal of Engineering, 3(1): (2015), 35-57.
  • [16] Papaschinopoulos G., Hatzifilippidis V. "On a max difference equation", Journal of Mathematical Analysis andApplications, (2001), 258-268.
  • [17] Papaschinopoulos G., Schinas J., Hatzifilippidis V. " Global behaviour of the solutions of a max-equation and of a system of two max-equation", Journal of Computational Analysis and Applications, 5, 2, (2003), 237-247.
  • [18] Patula W.T., Voulov H.D. "On a max type recursive relation with periodic coefficients", Journal of Difference Equations and Applications, 10, 3, (2004), 329-338.
  • [19] Stefanidou G., Papaschinopoulos G." The periodic nature of the positive solutions of a nonlinear fuzzy max--difference equation", Information Sciences, 176, (2006), 3694-3710.
  • [20] Stević S. "On the recursive sequence x_{n+1}=max{c,x_{n}^{p}/x_{n-1}^{p}}", Applied Mathematics Letters, vol. 21, No: 8, (2008), 791—796.
  • [21] Simsek D., Cinar C., Yalçınkaya I."On the solutions of the difference equation x_{n+1}=max{1/x_{n-1},x_{n-1}}, International Journal of Contemporary Mathematical Sciences, Vol.1, No: 9--12, (2006), 481—487.
  • [22] Simsek D., Demir B., Kurbanlı A. S. "x_{n+1}=max{(1/(x_{n})),((y_{n})/(x_{n}))}, y_{n+1}=max{(1/(y_{n})),((x_{n})/(y_{n}))} Denklem Sistemlerinin Çözümleri Üzerine", Ahmet Keleşoğlu Eğitim Fakültesi Dergisi, 28, (2009), 91-104.
  • [23] Simsek D., Demir B., Cinar, C. "On the Solutions of the System of Difference Equationsx_{n+1}=max{(A/(x_{n})),((y_{n})/(x_{n}))},y_{n+1}=max{(A/(y_{n})),((x_ {n})/(y_{n}))}", Discrete Dynamics in Nature and Society, Article ID 325296, (2009), 11.
  • [24] Simsek D., Kurbanlı A. S., Erdoğan M. E. "x(n+1) = max{1 \ x(n-1) ; y(n-1) \ x(n-1)} ; y(n+1) = max{1 \ y(n-1) ; x(n-1) \ y(n-1)} Fark Denklem Sisteminin Çözümleri", XXIII. Ulusal Matematik Sempozyumu, (2010), 153.
  • [25] Simsek D., Dogan, A. "Solutions Of The System Of Maximum Difference Equations", Manas Journal of Engineering, 2(2): (2014), 9-22.
  • [26] Simsek D., Eröz, M. “ x(n+1) = max {1/x(n-1), y(n)/x(n-1) }, y(n+1) = max {1/y(n-1), x(n)/y(n-1) } Maksimumlu Fark Denklem Sisteminin Çözümleri”, Manas Journal of Engineering, 3(2) (2015).
  • [27] Voulov H.D. "On the periodic character of some difference equations", Journal of Difference Equations and Applications, 8, (2002),799-810.
  • [28] Yalçınkaya I., Iricanin B.D., Çinar, C. "On a max-type difference equation", Discrete Dynamics in Nature and Society, (2007), Article ID 47264, 10.
  • [29] Yalçınkaya I., Çinar C., Atalay M. "On the solutions of systems of difference equations", Advances in Difference Equations, (2008), Article ID 143943, 9.

Maksimumlu Fark Denklem Sisteminin Çözümleri

Year 2016, Volume: 4 Issue: 2, 11 - 23, 01.10.2016

Abstract

Aşağıdaki fark denklem sisteminin çözümlerinin periyodikliği ve davranışları incelenmiştir.

References

  • [1] Amleh A.M. "Boundedness Periodicity and Stability of Some Difference Equations", PhD Thesis, University of Rhode Island, (1998).
  • [2] Çinar C., Stevic S., Yalçınkaya İ "On the positive solutions of reciprocal difference equation with minimum", Journal of Applied Mathematics and Computing, 17, (1-2), (2005), 307-314.
  • [3] Elaydi S."An Introduction to Difference Equations", Spinger-Verlag, New York, (1996).
  • [4] Elsayed E.M., Stevic S."On the max-type equation x_{n+1}=max{A/x_{n},x_{n-2}}", Nonlinear Analysis, TMA 71, (2009), 910-922.
  • [5] Elsayed E.M., Iricanin B., Stevic S. "On the max-type equation x_{n+1} = max{A_{n}/x_{n},x_{n-1}}", ARS Combin., (2010).
  • [6] Feuer J."Periodic solutions of the Lyness max equation", Journal of Mathematical Analysis and Applications, 288, (2003), 147-160.
  • [7] Gelişken A., Çinar C., Karataş R."A note on the periodicity of the Lyness max equation", Advances in Difference Equations, (2008), Article ID 651747, 5.
  • [8] Gelişken A., Çinar C., Yalçınkaya İ. "On the periodicity of a difference equation with maximum", Discrete Dynamics in Nature and Society, (2008), Article ID 820629, 11.
  • [9] Gelişken A., Çinar C., Kurbanlı A.S. "On the asymptotic behavior and periodic nature of a difference equation with maximum", Computers & Mathematics with Applications, 59, (2010), 898-902.
  • [10] Iricanin B., Elsayed, E.M. "On a max-type equation x_{n+1}=max{A/x_{n},x_{n-3}}", Discrete Dynamics in Nature and Society, (2010), Article ID 675413.
  • [11] Kulenevic M.R.S., Ladas G. "Dynamics of Second Order Rational Difference Equations with Open Problems and Conjecture",Boca Raton, London, (2002).
  • [12] Mishev D.P., Patula W.T., Voulov H.D. "A reciprocal difference equation with maximum", Computers & Mathematics with Applications, 43, (2002), 1021-1026.
  • [13] Moybe L.A. "Difference Equations with Public Health Applications", New York, USA, (2000).
  • [14] Огул Б., Шимшек Д." Система решение разностного уравнения", Весник Кыргызского Государственного Технического Университета, N 34, Бишкек, Кыргызстан, (2015).
  • [15] Ogul B., Simsek D. "  Maksimumlu Fark Denklem Sisteminin Çözümleri", Manas Journal of Engineering, 3(1): (2015), 35-57.
  • [16] Papaschinopoulos G., Hatzifilippidis V. "On a max difference equation", Journal of Mathematical Analysis andApplications, (2001), 258-268.
  • [17] Papaschinopoulos G., Schinas J., Hatzifilippidis V. " Global behaviour of the solutions of a max-equation and of a system of two max-equation", Journal of Computational Analysis and Applications, 5, 2, (2003), 237-247.
  • [18] Patula W.T., Voulov H.D. "On a max type recursive relation with periodic coefficients", Journal of Difference Equations and Applications, 10, 3, (2004), 329-338.
  • [19] Stefanidou G., Papaschinopoulos G." The periodic nature of the positive solutions of a nonlinear fuzzy max--difference equation", Information Sciences, 176, (2006), 3694-3710.
  • [20] Stević S. "On the recursive sequence x_{n+1}=max{c,x_{n}^{p}/x_{n-1}^{p}}", Applied Mathematics Letters, vol. 21, No: 8, (2008), 791—796.
  • [21] Simsek D., Cinar C., Yalçınkaya I."On the solutions of the difference equation x_{n+1}=max{1/x_{n-1},x_{n-1}}, International Journal of Contemporary Mathematical Sciences, Vol.1, No: 9--12, (2006), 481—487.
  • [22] Simsek D., Demir B., Kurbanlı A. S. "x_{n+1}=max{(1/(x_{n})),((y_{n})/(x_{n}))}, y_{n+1}=max{(1/(y_{n})),((x_{n})/(y_{n}))} Denklem Sistemlerinin Çözümleri Üzerine", Ahmet Keleşoğlu Eğitim Fakültesi Dergisi, 28, (2009), 91-104.
  • [23] Simsek D., Demir B., Cinar, C. "On the Solutions of the System of Difference Equationsx_{n+1}=max{(A/(x_{n})),((y_{n})/(x_{n}))},y_{n+1}=max{(A/(y_{n})),((x_ {n})/(y_{n}))}", Discrete Dynamics in Nature and Society, Article ID 325296, (2009), 11.
  • [24] Simsek D., Kurbanlı A. S., Erdoğan M. E. "x(n+1) = max{1 \ x(n-1) ; y(n-1) \ x(n-1)} ; y(n+1) = max{1 \ y(n-1) ; x(n-1) \ y(n-1)} Fark Denklem Sisteminin Çözümleri", XXIII. Ulusal Matematik Sempozyumu, (2010), 153.
  • [25] Simsek D., Dogan, A. "Solutions Of The System Of Maximum Difference Equations", Manas Journal of Engineering, 2(2): (2014), 9-22.
  • [26] Simsek D., Eröz, M. “ x(n+1) = max {1/x(n-1), y(n)/x(n-1) }, y(n+1) = max {1/y(n-1), x(n)/y(n-1) } Maksimumlu Fark Denklem Sisteminin Çözümleri”, Manas Journal of Engineering, 3(2) (2015).
  • [27] Voulov H.D. "On the periodic character of some difference equations", Journal of Difference Equations and Applications, 8, (2002),799-810.
  • [28] Yalçınkaya I., Iricanin B.D., Çinar, C. "On a max-type difference equation", Discrete Dynamics in Nature and Society, (2007), Article ID 47264, 10.
  • [29] Yalçınkaya I., Çinar C., Atalay M. "On the solutions of systems of difference equations", Advances in Difference Equations, (2008), Article ID 143943, 9.
There are 29 citations in total.

Details

Other ID JA76CF28JD
Journal Section Research Article
Authors

D. Şimşek This is me

M. Eröz This is me

B. Öğul This is me

Publication Date October 1, 2016
Published in Issue Year 2016 Volume: 4 Issue: 2

Cite

APA Şimşek, D., Eröz, M., & Öğul, B. (2016). Solutions of the System of Maximum Difference Equations. MANAS Journal of Engineering, 4(2), 11-23.
AMA Şimşek D, Eröz M, Öğul B. Solutions of the System of Maximum Difference Equations. MJEN. October 2016;4(2):11-23.
Chicago Şimşek, D., M. Eröz, and B. Öğul. “Solutions of the System of Maximum Difference Equations”. MANAS Journal of Engineering 4, no. 2 (October 2016): 11-23.
EndNote Şimşek D, Eröz M, Öğul B (October 1, 2016) Solutions of the System of Maximum Difference Equations. MANAS Journal of Engineering 4 2 11–23.
IEEE D. Şimşek, M. Eröz, and B. Öğul, “Solutions of the System of Maximum Difference Equations”, MJEN, vol. 4, no. 2, pp. 11–23, 2016.
ISNAD Şimşek, D. et al. “Solutions of the System of Maximum Difference Equations”. MANAS Journal of Engineering 4/2 (October 2016), 11-23.
JAMA Şimşek D, Eröz M, Öğul B. Solutions of the System of Maximum Difference Equations. MJEN. 2016;4:11–23.
MLA Şimşek, D. et al. “Solutions of the System of Maximum Difference Equations”. MANAS Journal of Engineering, vol. 4, no. 2, 2016, pp. 11-23.
Vancouver Şimşek D, Eröz M, Öğul B. Solutions of the System of Maximum Difference Equations. MJEN. 2016;4(2):11-23.

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