Abstract
We obtain a characterization of Ulam stability for the linear difference equation with constant coefficients \(x_{n+p}=a_₁x_{n+p-1}+…+a_{p}x_{n}\) in locally convex spaces. Moreover, for the first order linear difference equation we determine the best Ulam constant.
Authors
Adela Novac
Technical University of Cluj-Napoca, Romania
Diana Otrocol
Technical University of Cluj-Napoca, Romania
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy
Dorian Popa
Technical University of Cluj-Napoca, Romania
Keywords
Ulam stability; difference equations; best constant; locally convex spaces
soon
Cite this paper as:
A. Novac, D. Otrocol, D. Popa, Ulam stability of a linear difference equation in locally convex spaces, Results Math., 76, 33 (2021). https://doi.org/10.1007/s00025-021-01344-2
About this paper
Print ISSN
Not available yet.
Online ISSN
Not available yet.
Google Scholar Profile
[1] Anderson, D.R., Onitsuka, M., Hyers–Ulam stability for a discrete time scale with two step sizes. Appl. Math. Comput. 344–345, 128–140 (2019),MathSciNet MATH Google Scholar
[2] Baias, A.R., Blaga, F., Popa, D., Best Ulam constant for a linear difference equation. Carpatian J. Math. 35(1), 13–21 (2019), MathSciNet MATH Google Scholar
[3] Brillouët-Belluot, N., Brzdȩk, J., Ciepliński, K., On Some Recent Developments in Ulam’s Type Stability, Abstract and Applied Analysis Volume 2012, Article ID 716936, 41p
[4] Brzdȩk, J., Popa, D., Raşa, I., Xu, B., Ulam Stability of Operators. Academic Press, Cambridge (2018), MATH Google Scholar
[5] Brzdȩk, J., Wojcek, P., On approximate solutions of some difference equation. Bull. Aust. Math. Soc. 95(3), 476–481 (2017), MathSciNet Article Google Scholar
[6] Brzdȩk, J., Popa, D., Xu, B., The Hyers–Ulam stability of the nonlinear recurrence. J. Math. Anal. Appl. 335, 443–449 (2007), MathSciNet Article Google Scholar
[7] Brzdȩk, J., Popa, D., Xu, B., Note on the nonstability of the nonlinear recurrence. Abh. Math. Sem. Univ. Hamburg 76, 183–189 (2006), MathSciNet Article Google Scholar
[8] Brzdȩk, J., Popa, D., Xu, B., On nonstability of the linear recurrence of order one. J. Math. Anal. Appl. 367, 146–153 (2010), MathSciNet Article Google Scholar
[9] Hyers, D.H., On the stability of the linear functional equations. In: Proc. Nat, Acad. Sci., USA, 27, pp. 222–224 (1941)
[10] Jameson, G.J.O., Convex series. Proc. Camb. Phil. Soc. 37–47, (1972)
[11] Moslehian, M.S., Popa, D., On the stability of the first-order linear recurrence in topological vector spaces. Nonlinear Anal. 73, 2792–2799 (2010), MathSciNet Article Google Scholar
[12] Onitsuka, M., Influence of the stepsize on Hyers-Ulam stability of first order homogeneous linear difference equations. Int. J. Differ. Equ. 12(2), 281–302 (2017), MathSciNet Google Scholar
[13] Polya, G., Szegö, G., Aufgaben und Lehrsatze aus der Analysis I. Julius Springer, Berlin (1925), Book Google Scholar
[14] Popa, D., Hyers–Ulam stability of the linear recurrence with constant coefficient. Adv. Differ. Equ.-NY, 101–107 (2005)
[15] Popa, D., Hyers–Ulam–Rassias stability of the linear recurrence. J. Math. Anal. Appl. 309, 591–597 (2005), MathSciNet Article Google Scholar
[16] Popa, D., Raşa, I., Best constant in stability of some positive linear operators. Aequ. Math. 90, 719–726 (2016), MathSciNet Article Google Scholar
[17] Rudin, W., Functional analysis. In: International Series in Pure and Applied Mathematics, 2nd ed. McGraw-Hill Inc., New York (1991)
[18] Ulam, S.M., Problems in Modern Mathematics. Wiley, New York (1964), MATH Google Scholar