Research Article
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Year 2022, Volume: 71 Issue: 1, 68 - 78, 30.03.2022
https://doi.org/10.31801/cfsuasmas.861915

Abstract

References

  • Bede, B., Mathematics of Fuzzy Sets and Fuzzy Logic, Springer, New York, 2013.
  • Chrysafis, K. A., Papadopoulos, B. K., Papaschinopoulos, G., On the fuzzy difference equations of finance, Fuzzy Sets Syst., 159 (2008), 3259–3270. https://doi:10.1016/j.fss.2008.06.007
  • Deeba, E., De Korvin, A., Koh, E. L., A fuzzy difference equation with an application, J. Differ. Equ. Appl., 2 (1996), 365–374. https://doi.org/10.1080/10236199608808071
  • Deeba, E., De Korvin, A., Analysis by fuzzy difference equations of a model of CO2 level in blood, Appl. Math. Lett., 12 (1999), 33–40. https://doi.org/10.1016/S0893-9659(98)00168-2
  • El-Owaidy, H. M., Ahmed, A. M., Youssef, A. M., The dynamics of the recursive sequence $x_{n+1}=(\alpha x_{n-1})/(\beta +\gamma x_{n-2}^{p})$, Appl. Math. Lett., 18(9) (2005), 1013-1018. https://doi.org/10.1016/j.aml.2003.09.014
  • Elsayed, E. M., On the solutions and periodic nature of some systems of difference equations, Int. J. Biomath., 7 (2014), 26 pages. https://doi.org/10.1142/S1793524514500673
  • Gumus, M., Soykan, Y., Global character of a six-dimensional nonlinear system of difference equations, Discrete Dyn. Nat. Soc., Article ID 6842521 (2016), 7 pages. https://doi.org/10.1155/2016/6842521
  • Klir, G., Yuan, B., Fuzzy Sets and Fuzzy Logic Theory and Applications, Prentice Hall, New Jersey, 1995.
  • Hatir, E., Mansour, T., Yalcinkaya, I., On a fuzzy difference equation, Util. Math., 93 (2014), 135-151.
  • Negoita, C. V., Ralescu, D., Applications of Fuzzy Sets to Systems Analysis, Birkhauser, Verlag, Besel, 1975.
  • Papaschinopoulos, G., Papadopoulos, B. K., On the fuzzy difference equation $x_{n+1}=A+B/x_{n}$, Soft Comput., 6 (2002), 456-461. https://doi.org/10.1007/s00500-001-0161-7
  • Papaschinopoulos, G., Papadopoulos, B. K., On the fuzzy difference equation $x_{n+1}=A+x_{n}/x_{n-m}$, Fuzzy Sets Syst., 129 (2002), 73-81. https://doi.org/10.1016/S0165- 0114(01)00198-1
  • Stefanidou, G., Papaschinopoulos, G., A fuzzy difference equation of a rational form, J. Nonlinear Math. Phys., 12 (2005), 300–315. https://doi.org/10.2991/jnmp.2005.12.s2.21
  • Pielou, E. C., Population and Community Ecology: Principles and Methods, CRC Press, London, 1974.
  • Popov, E. P., Automatic Regulation and Control, (Russian) Nauka, Moscow, 1966.
  • Wu, C., Zhang, B., Embedding problem of noncompact fuzzy number space $E^{∼}$, Fuzzy Sets Syst., 105 (1999), 165-169. https://doi.org/10.1016/S0165-0114(97)00218-2
  • Yalcinkaya, I., Atak, N., Tollu, D. T., On a third-order fuzzy difference equation, J. Prime Res. Math., 17(1) (2021), 59-69. http://jprm.sms.edu.pk/on-a-third-order-fuzzy-difference equation.

On a nonlinear fuzzy difference equation

Year 2022, Volume: 71 Issue: 1, 68 - 78, 30.03.2022
https://doi.org/10.31801/cfsuasmas.861915

Abstract

In this paper we investigate the existence, the boundedness and the
asymptotic behavior of the positive solutions of the fuzzy difference
equation

\[z_{n+1}=\dfrac{Az_{n-1}}{1+z_{n-2}^{p}},~n\in\mathbb{N}_{0}\]

where (zn)(zn) is a sequence of positive fuzzy numbers, AA and the initial
conditions zjz−j (j=0,1,2) (j=0,1,2) are positive fuzzy numbers and
pp is a positive integer.

References

  • Bede, B., Mathematics of Fuzzy Sets and Fuzzy Logic, Springer, New York, 2013.
  • Chrysafis, K. A., Papadopoulos, B. K., Papaschinopoulos, G., On the fuzzy difference equations of finance, Fuzzy Sets Syst., 159 (2008), 3259–3270. https://doi:10.1016/j.fss.2008.06.007
  • Deeba, E., De Korvin, A., Koh, E. L., A fuzzy difference equation with an application, J. Differ. Equ. Appl., 2 (1996), 365–374. https://doi.org/10.1080/10236199608808071
  • Deeba, E., De Korvin, A., Analysis by fuzzy difference equations of a model of CO2 level in blood, Appl. Math. Lett., 12 (1999), 33–40. https://doi.org/10.1016/S0893-9659(98)00168-2
  • El-Owaidy, H. M., Ahmed, A. M., Youssef, A. M., The dynamics of the recursive sequence $x_{n+1}=(\alpha x_{n-1})/(\beta +\gamma x_{n-2}^{p})$, Appl. Math. Lett., 18(9) (2005), 1013-1018. https://doi.org/10.1016/j.aml.2003.09.014
  • Elsayed, E. M., On the solutions and periodic nature of some systems of difference equations, Int. J. Biomath., 7 (2014), 26 pages. https://doi.org/10.1142/S1793524514500673
  • Gumus, M., Soykan, Y., Global character of a six-dimensional nonlinear system of difference equations, Discrete Dyn. Nat. Soc., Article ID 6842521 (2016), 7 pages. https://doi.org/10.1155/2016/6842521
  • Klir, G., Yuan, B., Fuzzy Sets and Fuzzy Logic Theory and Applications, Prentice Hall, New Jersey, 1995.
  • Hatir, E., Mansour, T., Yalcinkaya, I., On a fuzzy difference equation, Util. Math., 93 (2014), 135-151.
  • Negoita, C. V., Ralescu, D., Applications of Fuzzy Sets to Systems Analysis, Birkhauser, Verlag, Besel, 1975.
  • Papaschinopoulos, G., Papadopoulos, B. K., On the fuzzy difference equation $x_{n+1}=A+B/x_{n}$, Soft Comput., 6 (2002), 456-461. https://doi.org/10.1007/s00500-001-0161-7
  • Papaschinopoulos, G., Papadopoulos, B. K., On the fuzzy difference equation $x_{n+1}=A+x_{n}/x_{n-m}$, Fuzzy Sets Syst., 129 (2002), 73-81. https://doi.org/10.1016/S0165- 0114(01)00198-1
  • Stefanidou, G., Papaschinopoulos, G., A fuzzy difference equation of a rational form, J. Nonlinear Math. Phys., 12 (2005), 300–315. https://doi.org/10.2991/jnmp.2005.12.s2.21
  • Pielou, E. C., Population and Community Ecology: Principles and Methods, CRC Press, London, 1974.
  • Popov, E. P., Automatic Regulation and Control, (Russian) Nauka, Moscow, 1966.
  • Wu, C., Zhang, B., Embedding problem of noncompact fuzzy number space $E^{∼}$, Fuzzy Sets Syst., 105 (1999), 165-169. https://doi.org/10.1016/S0165-0114(97)00218-2
  • Yalcinkaya, I., Atak, N., Tollu, D. T., On a third-order fuzzy difference equation, J. Prime Res. Math., 17(1) (2021), 59-69. http://jprm.sms.edu.pk/on-a-third-order-fuzzy-difference equation.
There are 17 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Research Articles
Authors

İbrahim Yalçınkaya 0000-0003-4546-4493

Vildan Çalışkan 0000-0003-4763-1689

Durhasan Turgut Tollu 0000-0002-3313-8829

Publication Date March 30, 2022
Submission Date January 15, 2021
Acceptance Date July 29, 2021
Published in Issue Year 2022 Volume: 71 Issue: 1

Cite

APA Yalçınkaya, İ., Çalışkan, V., & Tollu, D. T. (2022). On a nonlinear fuzzy difference equation. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 71(1), 68-78. https://doi.org/10.31801/cfsuasmas.861915
AMA Yalçınkaya İ, Çalışkan V, Tollu DT. On a nonlinear fuzzy difference equation. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. March 2022;71(1):68-78. doi:10.31801/cfsuasmas.861915
Chicago Yalçınkaya, İbrahim, Vildan Çalışkan, and Durhasan Turgut Tollu. “On a Nonlinear Fuzzy Difference Equation”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71, no. 1 (March 2022): 68-78. https://doi.org/10.31801/cfsuasmas.861915.
EndNote Yalçınkaya İ, Çalışkan V, Tollu DT (March 1, 2022) On a nonlinear fuzzy difference equation. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71 1 68–78.
IEEE İ. Yalçınkaya, V. Çalışkan, and D. T. Tollu, “On a nonlinear fuzzy difference equation”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 71, no. 1, pp. 68–78, 2022, doi: 10.31801/cfsuasmas.861915.
ISNAD Yalçınkaya, İbrahim et al. “On a Nonlinear Fuzzy Difference Equation”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71/1 (March 2022), 68-78. https://doi.org/10.31801/cfsuasmas.861915.
JAMA Yalçınkaya İ, Çalışkan V, Tollu DT. On a nonlinear fuzzy difference equation. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71:68–78.
MLA Yalçınkaya, İbrahim et al. “On a Nonlinear Fuzzy Difference Equation”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 71, no. 1, 2022, pp. 68-78, doi:10.31801/cfsuasmas.861915.
Vancouver Yalçınkaya İ, Çalışkan V, Tollu DT. On a nonlinear fuzzy difference equation. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71(1):68-7.

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

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