The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
권호 표지
DOI QR코드

DOI QR Code

ON THE STABILITY OF THE FUNCTIONAL EQUATION g(x + y + xy) = g(x) + f(y) + xf(y) + yg(x)

  • Received : 2019.04.12
  • Accepted : 2019.11.21
  • Published : 2020.02.29
Download PDF
⟨ Previous Next ⟩

Abstract

In this note, we investigate the Hyers-Ulam stability and the hyperstability of the Pexider type functional equation g(x + y + xy) = g(x) + f(y) + xf(y) + yg(x).

Keywords

References

  1. T. Aoki: On the stability of the linear transformation in Banach spaces. J. Math. Soc. Japan 2 (1950), 64-66. https://doi.org/10.2969/jmsj/00210064
  2. P. Gavruta: A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings. J. Math. Anal. Appl. 184 (1994), 431-436. https://doi.org/10.1006/jmaa.1994.1211
  3. D.H. Hyers: On the stability of the linear functional equation. Proc. Natl. Acad. Sci. 27 (1941), 222-224. https://doi.org/10.1073/pnas.27.4.222
  4. Y.-S. Jung: On the stability of higher ring left derivations. Indian J. Pure Appl. Math. 47 (2016), no. 3, 523-533. https://doi.org/10.1007/s13226-016-0201-8
  5. Gy. Maksa: Problems 18, In 'Report on the 34th ISFE'. Aequationes Math. 53 (1997), 194.
  6. Zs. Pales: Remark 27, In 'Report on the 34th ISFE'. Aequationes Math. 53 (1997), 200-201
  7. Th.M. Rassias: On the stability of the linear mapping in Banach spaces. Proc. Amer. Math. Soc. 72 (1978), 297-300. https://doi.org/10.1090/S0002-9939-1978-0507327-1
  8. F. Skof: Sull'approssimazione delle appliazioni localmente ${\delta}$-additive. Atti Accad. Sc. Torino. 117 (1983), 377-389
  9. J. Tabor: Remarks 20, In 'Report on the 34th ISFE'. Aequationes Math. 53 (1997), 194-196
  10. S.M. Ulam: A Collection of Mathematical Problems. Interscience Publ., New York, 1960.