PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Hyers-Ulam stability of first-order homogeneous linear dynamic equations on time scales

Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We establish the Hyers-Ulam stability (HUS) of certain first-order linear constant coefficient dynamic equations on time scales, which include the continuous (step size zero) and the discrete (step size constant and nonzero) dynamic equations as important special cases. In particular, for certain parameter values in relation to the graininess of the time scale, we find the minimum HUS constants. A few nontrivial examples are provided. Moreover, an application to a perturbed linear dynamic equation is also included.
Wydawca
Rocznik
Strony
198--210
Opis fizyczny
Bbliogr. 28 poz., wykr.
Twórcy
  • Department of Mathematics, Concordia College, Moorhead, MN 56562 USA
autor
  • Department of Applied Mathematics, Okayama University of Science, Okayama 700-0005 Japan
Bibliografia
  • [1] Ulam S. M., A Collection of the Mathematical Problems, Interscience, New York, 1960
  • [2] Hyers D. H., On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A., 1941, 27, 222-224
  • [3] Rassias Th. M., On the stability of linear mapping in Banach spaces, Proc. Amer. Math. Soc., 1978, 72, 297-300
  • [4] Alsina C., Ger R., On some inequalities and stability results related to the exponential function, J. Inequal. Appl., 1998, 2, 373-380
  • [5] András S., Mészáros A. R., Ulam-Hyers stability of dynamic equations on time scales via Picard operators, Appl. Math. Computation, 2013, 219(9), 4853-4864
  • [6] Brzdęk J., Popa D., Raşa I., Xu B., Ulam Stability of Operators, A volume in Mathematical Analysis and its Applications, Academic Press, 2018
  • [7] Jung S.-M., Hyers-Ulam stability of linear differential equations of first order (I), Int. J. Appl. Math. Stat., 2007, 7, 96-100
  • [8] Jung S.-M., Hyers-Ulam stability of linear differential equation of the first order (III), J. Math. Anal. Appl., 2005, 311, 139-146
  • [9] Jung S.-M., Hyers-Ulam stability of linear differential equations of first order (II), Appl. Math. Lett., 2006, 19, 854-858
  • [10] Jung S.-M., Hyers-Ulam stability of a system of first order linear differential equations with constant coeflcients, J. Math. Anal. Appl., 2006, 320, 549-561
  • [11] Jung S.-M., Kim B., Rassias Th. M., On the Hyers-Ulam stability of a system of Euler differential equations of first order, Tamsui Oxford J. Math. Sciences, 2008, 24(4), 381-388
  • [12] Miura T., Miyajima S., Takahasi S.-E., A characterization of Hyers-Ulam stability of first order linear differential operators, J. Math. Anal. Appl., 2003, 286(1), 136-146
  • [13] Miura T., Miyajima S., Takahasi S.-E., Hyers-Ulam stability of linear differential operator with constant coeflcients, Math. Nachr., 2003, 258, 90-96
  • [14] Rus I. A., Ulam stability of ordinary differential equations, Stud. Univ. Babeş-Bolyai Math., 2009, 54, 125-134
  • [15] Wang G., Zhou M., Sun L., Hyers-Ulam stability of linear differential equations of first order, Appl. Math. Lett., 2008, 21, 1024-1028
  • [16] Onitsuka M., Shoji T., Hyers-Ulam stability of first-order homogeneous linear differential equations with a real-valued coefficient, Appl. Math. Lett., 2017, 63, 102-108
  • [17] Onitsuka M., Influence of the stepsize on Hyers-Ulam stability of first-order homogeneous linear difference equations, Int. J. Difference Equ., 2017, 12(2), 281-302
  • [18] Brzdęk J., Wójcik P., On approximate solutions of some difference equations, Bull. Aust. Math. Soc., 2017, 95(3), 476-481
  • [19] Hua L., Li Y., Feng J., On Hyers-Ulam stability of dynamic integral equation on time scales, Math. Aeterna, 2014, 4(6), 559-571
  • [20] Jung S.-M., Nam Y. W., Hyers-Ulam stability of Pielou logistic difference equation, J. Nonlinear Sci. Appl., 2017, 10(6), 3115-3122
  • [21] Nam Y. W., Hyers-Ulam stability of hyperbolic Möbius difference equation, 2017, arXiv:1708.08662v1
  • [22] Rasouli H., Abbaszadeh S., Eshaghi M., Approximately linear recurrences, J. Appl. Anal., 2018, 24(1), 81-85
  • [23] Brillouët-Belluot N., Brzdęk J., Ciepliński K., On some recent developments in Ulam’s type stability, Abstr. Appl. Anal., 2012, Article ID 716936
  • [24] Shen Y. H., The Ulam stability of first order linear dynamic equations on time scales, Results Math., 2017, 72(4), 1881-1895
  • [25] Bohner M., Peterson A., Dynamic Equations on Time Scales, An Introduction with Applications, Birkhäuser, Boston, 2001
  • [26] Anderson D. R., Otto J., Hyers-Ulam stability of linear differential equations with vanishing coeflcients, Communications Appl. Anal., 2015, 19, 15-30
  • [27] Michel A. N., Hou L., Liu D., Stability of Dynamical Systems, On the Role of Monotonic and Non-monotonic Lyapunov Functions, Second edition, Systems & Control, Foundations & Applications, Birkhäuser/Springer, Cham, 2015
  • [28] Yoshizawa T., Stability Theory by Liapunov’s Second Method, The Mathematical Society of Japan, Tokyo, 1966
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-71fd819e-d2f0-45be-a393-15aa5b7707a2
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.