Hyers-Ulam Stability of a System of First Order Linear Recurrences with Constant Coefficients
Joint Authors
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-5, 5 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-03-02
Country of Publication
Egypt
No. of Pages
5
Main Subjects
Abstract EN
We study the Hyers-Ulam stability in a Banach space X of the system of first order linear difference equations of the form xn+1=Axn+dn for n∈N0 (nonnegative integers), where A is a given r×r matrix with real or complex coefficients, respectively, and (dn)n∈N0 is a fixed sequence in Xr.
That is, we investigate the sequences (yn)n∈N0 in Xr such that δ∶=supn∈N0yn+1-Ayn-dn<∞ (with the maximum norm in Xr) and show that, in the case where all the eigenvalues of A are not of modulus 1, there is a positive real constant c (dependent only on A) such that, for each such a sequence (yn)n∈N0, there is a solution (xn)n∈N0 of the system with supn∈N0yn-xn≤cδ.
American Psychological Association (APA)
Xu, Bing& Brzdek, Janusz. 2015. Hyers-Ulam Stability of a System of First Order Linear Recurrences with Constant Coefficients. Discrete Dynamics in Nature and Society،Vol. 2015, no. 2015, pp.1-5.
https://search.emarefa.net/detail/BIM-1060440
Modern Language Association (MLA)
Xu, Bing& Brzdek, Janusz. Hyers-Ulam Stability of a System of First Order Linear Recurrences with Constant Coefficients. Discrete Dynamics in Nature and Society No. 2015 (2015), pp.1-5.
https://search.emarefa.net/detail/BIM-1060440
American Medical Association (AMA)
Xu, Bing& Brzdek, Janusz. Hyers-Ulam Stability of a System of First Order Linear Recurrences with Constant Coefficients. Discrete Dynamics in Nature and Society. 2015. Vol. 2015, no. 2015, pp.1-5.
https://search.emarefa.net/detail/BIM-1060440
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1060440