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STABILITY CRITERION FOR DIFFERENCE EQUATIONS INVOLVING GENERALIZED DIFFERENCE OPERATOR

Year 2018, Volume: 67 Issue: 1, 248 - 261, 01.02.2018
https://doi.org/10.1501/Commua1_0000000847

Abstract

In this study, some necessary and su¢ cient conditions are givenfor the stability of some class of diğerence equations including generalizeddiğerence operator. For this, Schur-Cohn criteria is used and some examplesare given to verify the results obtained

References

  • Agarwal,R. P., Diğerence Equations and Inequalities, Marcel Dekker, New York, 2000. µCermák, J., Jánskı, J. & Kundrát, P., On necessary and su¢ cient conditions for the asymp- totic stability of higher order linear diğerence equations, Journal of Diğ erence Equations and Applications (2011),Vol. 18, No. 11, 1781-1800.
  • Camouzis, E., Ladas, G., Dynamics of Third Order Rational diğerence Equations with open Problems and Conjectures, Chapman &Hall, 2008.
  • Clark,C. W., A delay-recruitment model of populations dynamics with application to baleen whale populations, J. Math. Biol. 3 (1976), 381-391.
  • Dannan, F. M. and Elaydi, S., Asymptotic stability of linear diğerence equation of advanced type, J. Comput. Anal. Appl.6 (2004), 173-187.
  • Elaydi, S., An Introduction to Diğerence Equations, 3nd ed., Springer, 2000.
  • Kelley, W. G., Peterson, A. C., Diğerence Equations. An Introduction with Applications, Academic Press inc, 1991.
  • Kuruklis,S. A., The asymptotic stability of x(n+1) - ax(n) + bx(n-k) = 0, J.Math. Anal. Appl., 188, (1994), 719–731.
  • Levin, S. and May, R., A Note on Diğerence-Delay Equations, Theoretical Population Biol., (1976), 178-187.
  • Liz, E., On explicit conditions for the asymptotic stability of linear higher order diğerence equations, J. Math. Anal. Appl. 303 (2005), 492–498.
  • Matsunaga H. and Hara, T., The asymptotic stability of a two-dimensional linear delay diğerence equation, Dynam. Contin. Discrete Impuls. Systems, 6 (1999), 465–473.
  • Matsunaga, H., Ogita, R., Murakami, K., Asymtotic behaviour of a system of higher order linear diğerence equations, Nonlinear Analysis 47(2001), 4667-4677.
  • Mickens, R. E., Diğerence Equations, Van Nostrand Reinhold Company, New York, 1990.
  • Popenda,J. and Szmanda B., On the oscillation of solutions of certain diğerence equations, Demonstratio Mathematica, (1984), XVII:153-164.
  • Popenda, J., Oscillation and nonoscillation theorems for second-order diğerence equations, J. Math. Anal. Appl., 123(1),(1987), 34-38.
  • Current address : Murat GEVGE¸SO ¼GLU: Department of Mathematics, Faculty of Arts & Sciences, Kastamonu University, Kastamonu, TURKEY E-mail address : mgevgesoglu@kastamomnu.edu.tr Current address : Ya¸sar BOLAT: Department of Mathematics, Faculty of Arts & Sciences, Kastamonu University, Kastamonu, TURKEY E-mail address : ybolat@kastamonu.edu.tr
Year 2018, Volume: 67 Issue: 1, 248 - 261, 01.02.2018
https://doi.org/10.1501/Commua1_0000000847

Abstract

References

  • Agarwal,R. P., Diğerence Equations and Inequalities, Marcel Dekker, New York, 2000. µCermák, J., Jánskı, J. & Kundrát, P., On necessary and su¢ cient conditions for the asymp- totic stability of higher order linear diğerence equations, Journal of Diğ erence Equations and Applications (2011),Vol. 18, No. 11, 1781-1800.
  • Camouzis, E., Ladas, G., Dynamics of Third Order Rational diğerence Equations with open Problems and Conjectures, Chapman &Hall, 2008.
  • Clark,C. W., A delay-recruitment model of populations dynamics with application to baleen whale populations, J. Math. Biol. 3 (1976), 381-391.
  • Dannan, F. M. and Elaydi, S., Asymptotic stability of linear diğerence equation of advanced type, J. Comput. Anal. Appl.6 (2004), 173-187.
  • Elaydi, S., An Introduction to Diğerence Equations, 3nd ed., Springer, 2000.
  • Kelley, W. G., Peterson, A. C., Diğerence Equations. An Introduction with Applications, Academic Press inc, 1991.
  • Kuruklis,S. A., The asymptotic stability of x(n+1) - ax(n) + bx(n-k) = 0, J.Math. Anal. Appl., 188, (1994), 719–731.
  • Levin, S. and May, R., A Note on Diğerence-Delay Equations, Theoretical Population Biol., (1976), 178-187.
  • Liz, E., On explicit conditions for the asymptotic stability of linear higher order diğerence equations, J. Math. Anal. Appl. 303 (2005), 492–498.
  • Matsunaga H. and Hara, T., The asymptotic stability of a two-dimensional linear delay diğerence equation, Dynam. Contin. Discrete Impuls. Systems, 6 (1999), 465–473.
  • Matsunaga, H., Ogita, R., Murakami, K., Asymtotic behaviour of a system of higher order linear diğerence equations, Nonlinear Analysis 47(2001), 4667-4677.
  • Mickens, R. E., Diğerence Equations, Van Nostrand Reinhold Company, New York, 1990.
  • Popenda,J. and Szmanda B., On the oscillation of solutions of certain diğerence equations, Demonstratio Mathematica, (1984), XVII:153-164.
  • Popenda, J., Oscillation and nonoscillation theorems for second-order diğerence equations, J. Math. Anal. Appl., 123(1),(1987), 34-38.
  • Current address : Murat GEVGE¸SO ¼GLU: Department of Mathematics, Faculty of Arts & Sciences, Kastamonu University, Kastamonu, TURKEY E-mail address : mgevgesoglu@kastamomnu.edu.tr Current address : Ya¸sar BOLAT: Department of Mathematics, Faculty of Arts & Sciences, Kastamonu University, Kastamonu, TURKEY E-mail address : ybolat@kastamonu.edu.tr
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Details

Primary Language English
Journal Section Research Articles
Authors

Murat Gevgeşoğlu This is me

Yaşar Bolat This is me

Publication Date February 1, 2018
Published in Issue Year 2018 Volume: 67 Issue: 1

Cite

APA Gevgeşoğlu, M., & Bolat, Y. (2018). STABILITY CRITERION FOR DIFFERENCE EQUATIONS INVOLVING GENERALIZED DIFFERENCE OPERATOR. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 67(1), 248-261. https://doi.org/10.1501/Commua1_0000000847
AMA Gevgeşoğlu M, Bolat Y. STABILITY CRITERION FOR DIFFERENCE EQUATIONS INVOLVING GENERALIZED DIFFERENCE OPERATOR. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2018;67(1):248-261. doi:10.1501/Commua1_0000000847
Chicago Gevgeşoğlu, Murat, and Yaşar Bolat. “STABILITY CRITERION FOR DIFFERENCE EQUATIONS INVOLVING GENERALIZED DIFFERENCE OPERATOR”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67, no. 1 (February 2018): 248-61. https://doi.org/10.1501/Commua1_0000000847.
EndNote Gevgeşoğlu M, Bolat Y (February 1, 2018) STABILITY CRITERION FOR DIFFERENCE EQUATIONS INVOLVING GENERALIZED DIFFERENCE OPERATOR. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67 1 248–261.
IEEE M. Gevgeşoğlu and Y. Bolat, “STABILITY CRITERION FOR DIFFERENCE EQUATIONS INVOLVING GENERALIZED DIFFERENCE OPERATOR”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 67, no. 1, pp. 248–261, 2018, doi: 10.1501/Commua1_0000000847.
ISNAD Gevgeşoğlu, Murat - Bolat, Yaşar. “STABILITY CRITERION FOR DIFFERENCE EQUATIONS INVOLVING GENERALIZED DIFFERENCE OPERATOR”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67/1 (February 2018), 248-261. https://doi.org/10.1501/Commua1_0000000847.
JAMA Gevgeşoğlu M, Bolat Y. STABILITY CRITERION FOR DIFFERENCE EQUATIONS INVOLVING GENERALIZED DIFFERENCE OPERATOR. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2018;67:248–261.
MLA Gevgeşoğlu, Murat and Yaşar Bolat. “STABILITY CRITERION FOR DIFFERENCE EQUATIONS INVOLVING GENERALIZED DIFFERENCE OPERATOR”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 67, no. 1, 2018, pp. 248-61, doi:10.1501/Commua1_0000000847.
Vancouver Gevgeşoğlu M, Bolat Y. STABILITY CRITERION FOR DIFFERENCE EQUATIONS INVOLVING GENERALIZED DIFFERENCE OPERATOR. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2018;67(1):248-61.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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