JOURNAL BROWSE
Search
Advanced SearchSearch Tips
HYERS-ULAM-RASSIAS STABILITY OF A SYSTEM OF FIRST ORDER LINEAR RECURRENCES
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
HYERS-ULAM-RASSIAS STABILITY OF A SYSTEM OF FIRST ORDER LINEAR RECURRENCES
Xu, Mingyong;
  PDF(new window)
 Abstract
In this paper we discuss the Hyers-Ulam-Rassias stability of a system of first order linear recurrences with variable coefficients in Banach spaces. The concept of the Hyers-Ulam-Rassias stability originated from Th. M. Rassias# stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300. As an application, the Hyers-Ulam-Rassias stability of a p-order linear recurrence with variable coefficients is proved.
 Keywords
Hyers-Ulam-Rassias stability;linear recurrence;sequence;product space;
 Language
English
 Cited by
1.
Hyers–Ulam stability and discrete dichotomy, Journal of Mathematical Analysis and Applications, 2015, 423, 2, 1738  crossref(new windwow)
2.
Hyers–Ulam stability and discrete dichotomy for difference periodic systems, Bulletin des Sciences Mathématiques, 2016, 140, 8, 908  crossref(new windwow)
 References
1.
R. P. Agarwal, B. Xu, and W. Zhang, Stability of functional equations in single variable, J. Math. Anal. Appl. 288 (2003), no. 2, 852-869 crossref(new window)

2.
G. L. Forty, Hyers-Ulam stability of functional equations in several variables, Aequationes Math. 50 (1995), no. 1-2, 143-190 crossref(new window)

3.
G. L. Forty, Comments on the core of the direct method for proving Hyers-Ulam stability of functional equations, J. Math. Anal. Appl. 295 (2004), no. 1, 127-133 crossref(new window)

4.
R. Ger, Superstability is not natural, In Report of the twenty-sixth International Symposium on Functional Equations, Aequationes Math. 37 (1989), 68

5.
D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA 27 (1941), 222-224 crossref(new window)

6.
D. H. Hyers and Th. M. Rassias, Approximate homomorphisms, Aequationes Math. 44 (1992), no. 2-3, 125-153 crossref(new window)

7.
Y. H. Lee and K. W. Jun, A generalization of the Hyers-Ulam-Rassias stability of Jensen's equation, J. Math. Anal. Appl. 238 (1999), no. 1, 305-315 crossref(new window)

8.
K. Nikodem, The stability of the Pexider equation, Ann. Math. Sil. No. 5 (1991), 91-93

9.
D. Popa, Hyers-Ulam-Rassias stability of a linear recurrence, J. Math. Anal. Appl. 309 (2005), no. 2, 591-597 crossref(new window)

10.
D. Popa, Hyers-Ulam stability of the linear recurrence with constant coefficients, Adv. Difference Equ. 2005 (2005), no. 2, 101-107 crossref(new window)

11.
Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), no. 2, 297-300 crossref(new window)

12.
L. Szekelyhidi, The stability of the sine and cosine functional equations, Proc. Amer. Math. Soc. 110 (1990), no. 1, 109-115 crossref(new window)

13.
J. Tabor, On functions behaving like additive functions, Aequationes Math. 35 (1988), no. 2-3, 164-185 crossref(new window)

14.
T. Trif, On the stability of a general gamma-type functional equation, Publ. Math. Debrecen 60 (2002), no. 1-2, 47-61

15.
S. M. Ulam, Problems in modern mathematics, Science Editions John Wiley & Sons, Inc., New York, 1964