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Year 2019, Volume: 7 Issue: 1, 60 - 67, 18.06.2019

Dağıstan Şimşek Burak Oğul

https://izlik.org/JA32ZE65UZ

Abstract

References

  • Amleh A.M., Boundedness Periodicity and Stability of Some Difference Equations, PhD Thesis, University of Rhode Island, 1998.
  • Cinar C., Stevic S. and Yalçınkaya I., On the positive solutions of reciprocal difference equation with minimum, Journal of Applied Mathematics and Computing, 17(1-2), (2005) pp. 307-314.
  • Elaydi S., An Introduction to Difference Equations, Spinger-Verlag, New York, 1996.
  • Elsayed E.M. and Stevic S., On the max-type equation x_{n+1}=max{A/x_{n},x_{n-2}}, Nonlinear Analysis: Theory, Methods & Applications 71(3-4), (2009), pp. 910-922.
  • Elsayed E.M., Iricanin B. and Stevic S., On the max-type equation x_{n+1} = max{A_{n}/x_{n},x_{n-1}}, Ars Combinatoria 95, (2010), pp. 187-192.
  • Feuer J., Periodic solutions of the Lyness max equation, Journal of Mathematical Analysis and Applications 288(1), (2003), pp. 147-160.
  • Gelişken A., Cinar C. and Karataş R., A note on the periodicity of the Lyness max equation, Advances in Difference Equations 2008(1) (2007), pp. 651747.
  • Gelişken A., Cinar C. and Yalçınkaya I., On the periodicity of a difference equation with maximum, Discrete Dynamics in Nature and Society, 2008, (2008), pp. 820629.
  • Gelişken A., Cinar C., and Kurbanlı A.S., On the asymptotic behavior and periodic nature of a difference equation with maximum, Computers & mathematics with applications, 59(2) (2010), pp. 898-902.
  • Iricanin B. and 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, (2010), pp. 675413.
  • Kulenevic M.R.S and Ladas G., Dynamics of Second Order Rational Difference Equations with Open Problems and Conjecture, Boca Raton, London, 2002.
  • Mishev D.P., Patula W.T. and Voulov H.D., A reciprocal difference equation with maximum, Computers & Mathematics with Applications, 43, (2002), pp. 1021-1026.
  • Moybe L.A., Difference Equations with Public Health Applications, New York, USA, 2000.
  • Oğul B., Simsek D., System Solutions of Difference Equations x(n+1) = max (1/x(n-4), y(n-4)/x(n-4)), y(n+1) = max (1/y(n-4), x(n-4)/y(n-4)), Kyrgyz State Technicial University I. Razzakov Theoretical And Applied Scientific Technical Journal, No:1(34), 202-205, 2015.
  • Ogul B., Simsek D., Maksimumlu Fark Denklem Sisteminin Çözümleri, Manas Journal of Engineering, 3(1), (2015), pp. 35-57.
  • Papaschinopoulos G. and Hatzifilippidis V., On a max difference equation, Journal of Mathematical Analysis and Applications, 258, (2001), pp. 258-268.
  • Papaschinopoulos G., Schinas J. and 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), pp. 237-247.
  • Patula W.T. and Voulov H.T., On a max type recursive relation with periodic coefficients, Journal of Difference Equations and Applications, 10(3), (2004), pp. 329-338.
  • Simsek D., Camsitov, Solutions Of The Maximum Of Difference Equations, Manas Journal of Engineering, 6, (2018): 14-25.
  • Simsek D., Cinar C. and 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, 1(9), (2006), 481-487.
  • Simsek D., Demir B. and 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.
  • Simsek D., Demir B. and Cinar C., On the Solutions of the System of Difference Equations x_{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, 2009, (2009) pp. 325296.
  • 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, 153 pp, .04-07 Ağustos 2010, Erciyes Üniversitesi, 2010.
  • Simsek D., Dogan A., Solutions Of The System Of Maximum Difference Equations, Manas Journal of Engineering, 2(2), (2014), pp. 9-22.
  • Simsek D., Eroz M., Ogul B., x(n+1) = max (1/x(n),y(n)/z(n)), y(n+1) = max (1/y(n),z(n)/x(n)), z(n+1) = max (1/z(n),x(n)/y(n)) Maksimumlu Fark Denklem Sisteminin Çözümleri, Manas Journal of Engineering, 4(2), 11-23, 2016.
  • Simsek D., Ogul B., x(n+1) = max (1/x(n-1),y(n)/x(n-3)), y(n+1) = max (1/y(n-1),x(n)/y(n-3)) Maximum of Difference Equations, Manas Journal Of Engineering, 5(1), 14-28, 2017.
  • Stefanidou G. and Papaschinopoulos G., The periodic nature of the positive solutions of a nonlinear fuzzy max--difference equation, Information Sciences, 176, (2006), pp.3694-3710.
  • Stević S., On the recursive sequence x_{n+1}=max{c,x_{n}^{p}/x_{n-1}^{p}}", Applied Mathematics Letters, 21(8), (2008), pp. 791-796.
  • Teixeria C.T., Existence Stability Boundedness and Periodicity of Some Difference Equations, PhD Thesis, University of Rhode Island, 2000.
  • Valicenti S., Periodicity and Global Attractivity of Some Difference Equations, PhD Thesis, University of Rhode Island, 1999.
  • Voulov H.D., On the periodic character of some difference equations, Journal of Difference Equations and Applications, (8), (2002), pp. 799-810.
  • Voulov H.D., Periodic solutions to a difference equation with maximum, Proceedings of the American Mathematical Society, 131, (2002), pp. 2155-2160.
  • Yalçınkaya I., Iricanin B.D. and Cinar C., On a max-type difference equation, Discrete Dynamics in Nature and Society, 2007, (2007), pp. 47264.
  • Yalçınkaya I., Cinar C. and Atalay M., On the solutions of systems of difference equations, Advances in Difference Equations, (2008), (2008) pp. 143943.

Solutions of the system of maximum difference equations 1 1 3 3 1 1 max , ; max , n n n n n n n n y x x y xx yy + + − −   =   =  

Year 2019, Volume: 7 Issue: 1, 60 - 67, 18.06.2019

Dağıstan Şimşek Burak Oğul

https://izlik.org/JA32ZE65UZ

Abstract

This paper deals with the behaivour of the solutions of the max‐type system of difference equations

xn+1=max{1/xn-3,yn/xn}, yn+1=max{1/yn-3,xn/yn},

where the initial conditions are positive real numbers.

Keywords

Difference equation Maximum operators Semicycle

References

  • Amleh A.M., Boundedness Periodicity and Stability of Some Difference Equations, PhD Thesis, University of Rhode Island, 1998.
  • Cinar C., Stevic S. and Yalçınkaya I., On the positive solutions of reciprocal difference equation with minimum, Journal of Applied Mathematics and Computing, 17(1-2), (2005) pp. 307-314.
  • Elaydi S., An Introduction to Difference Equations, Spinger-Verlag, New York, 1996.
  • Elsayed E.M. and Stevic S., On the max-type equation x_{n+1}=max{A/x_{n},x_{n-2}}, Nonlinear Analysis: Theory, Methods & Applications 71(3-4), (2009), pp. 910-922.
  • Elsayed E.M., Iricanin B. and Stevic S., On the max-type equation x_{n+1} = max{A_{n}/x_{n},x_{n-1}}, Ars Combinatoria 95, (2010), pp. 187-192.
  • Feuer J., Periodic solutions of the Lyness max equation, Journal of Mathematical Analysis and Applications 288(1), (2003), pp. 147-160.
  • Gelişken A., Cinar C. and Karataş R., A note on the periodicity of the Lyness max equation, Advances in Difference Equations 2008(1) (2007), pp. 651747.
  • Gelişken A., Cinar C. and Yalçınkaya I., On the periodicity of a difference equation with maximum, Discrete Dynamics in Nature and Society, 2008, (2008), pp. 820629.
  • Gelişken A., Cinar C., and Kurbanlı A.S., On the asymptotic behavior and periodic nature of a difference equation with maximum, Computers & mathematics with applications, 59(2) (2010), pp. 898-902.
  • Iricanin B. and 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, (2010), pp. 675413.
  • Kulenevic M.R.S and Ladas G., Dynamics of Second Order Rational Difference Equations with Open Problems and Conjecture, Boca Raton, London, 2002.
  • Mishev D.P., Patula W.T. and Voulov H.D., A reciprocal difference equation with maximum, Computers & Mathematics with Applications, 43, (2002), pp. 1021-1026.
  • Moybe L.A., Difference Equations with Public Health Applications, New York, USA, 2000.
  • Oğul B., Simsek D., System Solutions of Difference Equations x(n+1) = max (1/x(n-4), y(n-4)/x(n-4)), y(n+1) = max (1/y(n-4), x(n-4)/y(n-4)), Kyrgyz State Technicial University I. Razzakov Theoretical And Applied Scientific Technical Journal, No:1(34), 202-205, 2015.
  • Ogul B., Simsek D., Maksimumlu Fark Denklem Sisteminin Çözümleri, Manas Journal of Engineering, 3(1), (2015), pp. 35-57.
  • Papaschinopoulos G. and Hatzifilippidis V., On a max difference equation, Journal of Mathematical Analysis and Applications, 258, (2001), pp. 258-268.
  • Papaschinopoulos G., Schinas J. and 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), pp. 237-247.
  • Patula W.T. and Voulov H.T., On a max type recursive relation with periodic coefficients, Journal of Difference Equations and Applications, 10(3), (2004), pp. 329-338.
  • Simsek D., Camsitov, Solutions Of The Maximum Of Difference Equations, Manas Journal of Engineering, 6, (2018): 14-25.
  • Simsek D., Cinar C. and 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, 1(9), (2006), 481-487.
  • Simsek D., Demir B. and 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.
  • Simsek D., Demir B. and Cinar C., On the Solutions of the System of Difference Equations x_{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, 2009, (2009) pp. 325296.
  • 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, 153 pp, .04-07 Ağustos 2010, Erciyes Üniversitesi, 2010.
  • Simsek D., Dogan A., Solutions Of The System Of Maximum Difference Equations, Manas Journal of Engineering, 2(2), (2014), pp. 9-22.
  • Simsek D., Eroz M., Ogul B., x(n+1) = max (1/x(n),y(n)/z(n)), y(n+1) = max (1/y(n),z(n)/x(n)), z(n+1) = max (1/z(n),x(n)/y(n)) Maksimumlu Fark Denklem Sisteminin Çözümleri, Manas Journal of Engineering, 4(2), 11-23, 2016.
  • Simsek D., Ogul B., x(n+1) = max (1/x(n-1),y(n)/x(n-3)), y(n+1) = max (1/y(n-1),x(n)/y(n-3)) Maximum of Difference Equations, Manas Journal Of Engineering, 5(1), 14-28, 2017.
  • Stefanidou G. and Papaschinopoulos G., The periodic nature of the positive solutions of a nonlinear fuzzy max--difference equation, Information Sciences, 176, (2006), pp.3694-3710.
  • Stević S., On the recursive sequence x_{n+1}=max{c,x_{n}^{p}/x_{n-1}^{p}}", Applied Mathematics Letters, 21(8), (2008), pp. 791-796.
  • Teixeria C.T., Existence Stability Boundedness and Periodicity of Some Difference Equations, PhD Thesis, University of Rhode Island, 2000.
  • Valicenti S., Periodicity and Global Attractivity of Some Difference Equations, PhD Thesis, University of Rhode Island, 1999.
  • Voulov H.D., On the periodic character of some difference equations, Journal of Difference Equations and Applications, (8), (2002), pp. 799-810.
  • Voulov H.D., Periodic solutions to a difference equation with maximum, Proceedings of the American Mathematical Society, 131, (2002), pp. 2155-2160.
  • Yalçınkaya I., Iricanin B.D. and Cinar C., On a max-type difference equation, Discrete Dynamics in Nature and Society, 2007, (2007), pp. 47264.
  • Yalçınkaya I., Cinar C. and Atalay M., On the solutions of systems of difference equations, Advances in Difference Equations, (2008), (2008) pp. 143943.
There are 34 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Dağıstan Şimşek This is me

Burak Oğul 0000-0002-3264-4340

Publication Date June 18, 2019
IZ https://izlik.org/JA32ZE65UZ
Published in Issue Year 2019 Volume: 7 Issue: 1

Cite

APA Şimşek, D., & Oğul, B. (2019). Solutions of the system of maximum difference equations 1 1 3 3 1 1 max , ; max , n n n n n n n n y x x y xx yy + + − −   =   =  . MANAS Journal of Engineering, 7(1), 60-67. https://izlik.org/JA32ZE65UZ
AMA 1.Şimşek D, Oğul B. Solutions of the system of maximum difference equations 1 1 3 3 1 1 max , ; max , n n n n n n n n y x x y xx yy + + − −   =   =  . MJEN. 2019;7(1):60-67. https://izlik.org/JA32ZE65UZ
Chicago Şimşek, Dağıstan, and Burak Oğul. 2019. “Solutions of the System of Maximum Difference Equations 1 1 3 3 1 1 Max , ; Max , N N N N N N N N Y X X Y Xx Yy + + − −   =   =  ”. MANAS Journal of Engineering 7 (1): 60-67. https://izlik.org/JA32ZE65UZ.
EndNote Şimşek D, Oğul B (June 1, 2019) Solutions of the system of maximum difference equations 1 1 3 3 1 1 max , ; max , n n n n n n n n y x x y xx yy + + − −   =   =  . MANAS Journal of Engineering 7 1 60–67.
IEEE [1]D. Şimşek and B. Oğul, “Solutions of the system of maximum difference equations 1 1 3 3 1 1 max , ; max , n n n n n n n n y x x y xx yy + + − −   =   =  ”, MJEN, vol. 7, no. 1, pp. 60–67, June 2019, [Online]. Available: https://izlik.org/JA32ZE65UZ
ISNAD Şimşek, Dağıstan - Oğul, Burak. “Solutions of the System of Maximum Difference Equations 1 1 3 3 1 1 Max , ; Max , N N N N N N N N Y X X Y Xx Yy + + − −   =   =  ”. MANAS Journal of Engineering 7/1 (June 1, 2019): 60-67. https://izlik.org/JA32ZE65UZ.
JAMA 1.Şimşek D, Oğul B. Solutions of the system of maximum difference equations 1 1 3 3 1 1 max , ; max , n n n n n n n n y x x y xx yy + + − −   =   =  . MJEN. 2019;7:60–67.
MLA Şimşek, Dağıstan, and Burak Oğul. “Solutions of the System of Maximum Difference Equations 1 1 3 3 1 1 Max , ; Max , N N N N N N N N Y X X Y Xx Yy + + − −   =   =  ”. MANAS Journal of Engineering, vol. 7, no. 1, June 2019, pp. 60-67, https://izlik.org/JA32ZE65UZ.
Vancouver 1.Dağıstan Şimşek, Burak Oğul. Solutions of the system of maximum difference equations 1 1 3 3 1 1 max , ; max , n n n n n n n n y x x y xx yy + + − −   =   =  . MJEN [Internet]. 2019 Jun. 1;7(1):60-7. Available from: https://izlik.org/JA32ZE65UZ

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