DOI QR코드

DOI QR Code

HYERS-ULAM-RASSIAS STABILITY OF A SYSTEM OF FIRST ORDER LINEAR RECURRENCES

  • Xu, Mingyong (DEPARTMENT OF MATHEMATICS SICHUAN UNIVERSITY)
  • Published : 2007.11.30

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

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 https://doi.org/10.1016/j.jmaa.2003.09.032
  2. G. L. Forty, Hyers-Ulam stability of functional equations in several variables, Aequationes Math. 50 (1995), no. 1-2, 143-190 https://doi.org/10.1007/BF01831117
  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 https://doi.org/10.1016/j.jmaa.2004.03.011
  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 https://doi.org/10.1073/pnas.27.4.222
  6. D. H. Hyers and Th. M. Rassias, Approximate homomorphisms, Aequationes Math. 44 (1992), no. 2-3, 125-153 https://doi.org/10.1007/BF01830975
  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 https://doi.org/10.1006/jmaa.1999.6546
  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 https://doi.org/10.1016/j.jmaa.2004.10.013
  10. D. Popa, Hyers-Ulam stability of the linear recurrence with constant coefficients, Adv. Difference Equ. 2005 (2005), no. 2, 101-107 https://doi.org/10.1155/ADE.2005.101
  11. Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), no. 2, 297-300 https://doi.org/10.1090/S0002-9939-1978-0507327-1
  12. L. Szekelyhidi, The stability of the sine and cosine functional equations, Proc. Amer. Math. Soc. 110 (1990), no. 1, 109-115 https://doi.org/10.1090/S0002-9939-1990-1015685-2
  13. J. Tabor, On functions behaving like additive functions, Aequationes Math. 35 (1988), no. 2-3, 164-185 https://doi.org/10.1007/BF01830942
  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

Cited by

  1. Hyers–Ulam stability and discrete dichotomy vol.423, pp.2, 2015, https://doi.org/10.1016/j.jmaa.2014.10.082
  2. Hyers–Ulam stability and discrete dichotomy for difference periodic systems vol.140, pp.8, 2016, https://doi.org/10.1016/j.bulsci.2016.03.010