SavedAdd your journal

Journals / Results in Nonlinear Analysis / 2026 / Cilt: 1 Sayı: 1

On the global stability of some k-order difference equations

Vasile Berinde(Technical University of Cluj-Napoca, Department of Mathematics and Computer, Baia Mare)
Hafiz Fukhar-ud-din(King Fahd University of Petroleum And Minerals, Department of Mathematics and Statistics, Dhahra)
Mădălina Păcurar(Babeş-Bolyai University, Department of Statistics, Forecast and Mathematics, Faculty of Economics and Business Administration)
Pages
13–18
Publication Date
2018-03-15
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In this way, we can study the global stability for more general initial value problems associated with particular forms of difference equations.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We use two different techniques, one of them including fixed point tools, i.e., the Prešić type fixed point theorem, in order to study the asymptotic stability of some k-order difference equations for k = 1 and k = 2.
📊
Key Findings & Data:We use two different techniques, one of them including fixed point tools, i.e., the Prešić type fixed point theorem, in order to study the asymptotic stability of some k-order difference equations for k = 1 and k = 2.
💡
Conclusion & Impact:In this way, we can study the global stability for more general initial value problems associated with particular forms of difference equations.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Difference equation · Equilibrium point · Global attractor

Abstract

We use two different techniques, one of them including fixed point tools, i.e., the Prešić type fixed point theorem, in order to study the asymptotic stability of some k-order difference equations for k = 1 and k = 2. In this way, we can study the global stability for more general initial value problems associated with particular forms of difference equations.

🔖

Cite This Article

Berinde, V., Fukhar-ud-din, H., Păcurar, M. (2018). On the global stability of some k-order difference equations. Results in Nonlinear Analysis, Cilt: 1 Sayı: 1, 13–18. https://ajindex.com/articles/1537778

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (39)

  1. Abu-Saris, R. M., DeVault, R., Global stability of yn+1 = A + yn yn−k. Appl. Math. Lett. 16 (2003), no. 2, 173–178.
  2. Aloqeili, M., On the difference equation xn+1 = α + xp n xp n−1. J. Appl. Math. Comput. 25 (2007), no. 1-2, 375–382.
  3. Amleh, A. M., Grove, E. A., Ladas, G., Georgiou, D. A., On the recursive sequence xn+1 = α + xn−1/xn. J. Math. Anal. Appl. 233 (1999), no. 2, 790–798.
  4. Berinde, V., Exploring, Investigating and Discovering in Mathematics, Birkhäuser, Basel, 2004.
  5. Berinde, V., Iterative approximation of fixed points, Second edition. Lecture Notes in Mathematics, 1912. Springer, Berlin, 2007.
  6. Berinde, V., Păcurar, M., Stability of k-step fixed point iterative methods for some Prešić type contractive mappings. J. Inequal. Appl. 2014, 2014:149, 12 pp.
  7. Berinde, V., Păcurar, M., Two elementary applications of some Prešić type fixed point theorems. Creat. Math. Inform. 20 (2011), no. 1, 32–42
  8. Berinde, V., Păcurar, M., O metodă de tip punct fix pentru rezolvarea sistemelor ciclice, Gazeta Matematică, Seria B, 116 (2011), No. 3, 113-123
  9. Camouzis, E., DeVault, R., Ladas, G., On the recursive sequence xn+1 = −1 + (xn−1/xn). J. Differ. Equations Appl. 7 (2001), no. 3, 477–482.
  10. Cirić, L.B., Prešić, S.B., On Prešić type generalization of the Banach contraction mapping principle, Acta Math. Univ. Comenianae, 76 (2007), No. 2, 143-147
  11. Chen, Y.-Z., A Prešić type contractive condition and its applications, Nonlinear Anal. 71 (2009), no. 12, e2012–e2017
  12. DeVault, R., Ladas, G., Schultz, S. W., On the recursive sequence xn+1 = A/xn + 1/xn−2. Proc. Amer. Math. Soc. 126 (1998), no. 11, 3257–3261.
  13. Elabbasy, E. M., El-Metwally, H., Elsayed, E. M., On the difference equation xn+1 = axn − bxn/(cxn − dxn−1). Adv. Difference Equ. 2006, Art. ID 82579, 10 pp.
  14. El-Owaidy, H. M., Ahmed, A. M., Mousa, M. S., On asymptotic behaviour of the difference equation xn+1 = α+ xn−1p xnp. J. Appl. Math. Comput. 12 (2003), no. 1-2, 31–37.
  15. El-Owaidy, H. M., Ahmed, A. M., Mousa, M. S., On asymptotic behaviour of the difference equation xn+1 = α + xn−k xn. Appl. Math. Comput. 147 (2004), no. 1, 163–167.
  16. Kocić, V. L., Ladas, G., Global behavior of nonlinear difference equations of higher order with applications. Mathematics and its Applications, 256. Kluwer Academic Publishers Group, Dordrecht, 1993.
  17. Păcurar, M., Approximating common fixed points of Prešić-Kannan type operators by a multi-step iterative method, An. Ştiinţ,. Univ. "Ovidius" Constanţa Ser. Mat. 17 (2009), no. 1, 153–168
  18. Păcurar, M., Iterative Methods for Fixed Point Approximation, Risoprint, Cluj-Napoca, 2010
  19. Păcurar, M., A multi-step iterative method for approximating fixed points of Prešić-Kannan operators, Acta Math. Univ. Comen. New Ser., 79 (2010), No. 1, 77-88
  20. Păcurar, M., A multi-step iterative method for approximating common fixed points of Prešić-Rus type operators on metric spaces, Stud. Univ. Babeş-Bolyai Math. 55 (2010), no. 1, 149–162.
  21. Păcurar, M., Fixed points of almost Prešić operators by a k-step iterative method, An. Ştiint,. Univ. Al. I. Cuza Iaşi, Ser. Noua, Mat. 57 (2011), Supliment 199–210
  22. Păvăloiu, I., Rezolvarea ecuaţiilor prin interpolare, Editura Dacia, Cluj-Napoca, 1981
  23. Păvăloiu, I. and Pop, N., Interpolare şi aplicaţii, Risoprint, Cluj-Napoca, 2005
  24. Prešić, S.B., Sur une classe d’ inéquations aux différences finites et sur la convergence de certaines suites, Publ. Inst. Math. (Beograd)(N.S.), 5(19) (1965), 75–78
  25. Rus, I.A., An iterative method for the solution of the equation x = f(x,.,x), Rev. Anal. Numer. Théor. Approx., 10 (1981), No.1, 95–100
  26. Saleh, M.; Aloqeili, M., On the rational difference equation yn+1 = A + yn−k yn. Appl. Math. Comput. 171 (2005), no. 2, 862–869.
  27. Saleh, M., Aloqeili, M., On the rational difference equation yn+1 = A + yn yn−k. Appl. Math. Comput. 177 (2006), no. 1, 189–193.
  28. Stević, S., On the recursive sequence xn+1 = α + xp n−1 xp n. J. Appl. Math. Comput. 18 (2005), no. 1-2, 229–234.
  29. Stević, S., On the recursive sequence xn+1 = A + xp n/xp n−1. Discrete Dyn. Nat. Soc. 2007, Art. ID 34517, 9 pp.
  30. Stević, S., On the recursive sequence xn+1 = A + xp n/xr n−1. Discrete Dyn. Nat. Soc. 2007, Art. ID 40963, 9 pp.
  31. Stević, S., On the recursive sequence xn+1 = maxc, xp n xp n−1. Appl. Math. Lett. 21 (2008), no. 8, 791–796.
  32. Abu-Saris, R. M., DeVault, R., Global stability of yn+1 = A + yn yn−k. Appl. Math. Lett. 16 (2003), no. 2, 173–178.
  33. Aloqeili, M., On the difference equation xn+1 = α + xp n xp n−1. J. Appl. Math. Comput. 25 (2007), no. 1-2, 375–382.
  34. El-Owaidy, H. M., Ahmed, A. M., Mousa, M. S., On asymptotic behaviour of the difference equation xn+1 = α+ xn−1p xnp. J. Appl. Math. Comput. 12 (2003), no. 1-2, 31–37.
  35. El-Owaidy, H. M., Ahmed, A. M., Mousa, M. S., On asymptotic behaviour of the difference equation xn+1 = α + xn−k xn. Appl. Math. Comput. 147 (2004), no. 1, 163–167.
  36. Rus, I.A., An iterative method for the solution of the equation x = f(x,.,x), Rev. Anal. Numer. Théor. Approx., 10 (1981), No.1, 95–100
  37. Saleh, M.; Aloqeili, M., On the rational difference equation yn+1 = A + yn−k yn. Appl. Math. Comput. 171 (2005), no. 2, 862–869.
  38. Saleh, M., Aloqeili, M., On the rational difference equation yn+1 = A + yn yn−k. Appl. Math. Comput. 177 (2006), no. 1, 189–193.
  39. Stević, S., On the recursive sequence xn+1 = α + xp n−1 xp n. J. Appl. Math. Comput. 18 (2005), no. 1-2, 229–234.