Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

ON STABILITY OF THE FUNCTIONAL EQUATIONS HAVING RELATION WITH A MULTIPLICATIVE DERIVATION

  • Published : 2007.02.28
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we study the Hyers-Ulam-Rassias stability of the functional equations related to a multiplicative derivation.

Keywords

References

  1. R. Badora, Report of Meeting: The Thirty-fourth International Symposium on Functional Equations, June 10 to 19, 1996, Wista-Jawornik, Poland, Aequationes Math. 53 (1997), no. 1-2, 162-205 https://doi.org/10.1007/BF02215972
  2. C. Borelli, On Hyers-Ulam stability for a class of functional equations, Aequationes Math. 54 (1997), no. 1-2, 74-86 https://doi.org/10.1007/BF02755447
  3. I.-S. Chang and Y.-S. Jung, Stability of a functional equation deriving from cubic and quadratic functions, J. Math. Anal. Appl. 283 (2003), no. 2, 491-500 https://doi.org/10.1016/S0022-247X(03)00276-2
  4. I.-S. Chang, E.-H. Lee, and H.-M. Kim, On Hyers-Ulam-Rassias stability of a quadratic functional equation, Math. Inequal. Appl. 6 (2003), no. 1, 87-95
  5. S. Czerwik, On the stability of the quadratic mapping in normed spaces, Abh. Math. Sem. Univ. Hamburg 62 (1992), 59-64 https://doi.org/10.1007/BF02941618
  6. Z. Gajda, On stability of additive mappings, Internat. J. Math. Math. Sci. 14 (1991), no. 3, 431-434 https://doi.org/10.1155/S016117129100056X
  7. P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), no. 3, 431-436 https://doi.org/10.1006/jmaa.1994.1211
  8. D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A. 27 (1941). 222-224
  9. D. H. Hyers, G. Isac, and Th. M. Rassias, Stability of Functional equation in Several Variables, Progress in Nonlinear Differential Equations and their Applications, 34. Birkhauser Boston, Inc., Boston, MA, 1998
  10. D. H. Hyers, G. Isac, and Th. M. Rassias, On the asymptoticity aspect of Hyers-Ulam stability of mappings, Proc. Amer. Math. Soc. 126 (1998), no. 2, 425-430 https://doi.org/10.1090/S0002-9939-98-04060-X
  11. D. H. Hyers and Th. M. Rassias, Approximate homomorphisms, Aequationes Math. 44 (1992), no. 2-3, 125-153 https://doi.org/10.1007/BF01830975
  12. K.-W. Jun and Y.-H. Lee, On the Hyers-Ulam-Rassias stability of a pexiderized quadratic inequality, Math. Inequal. Appl. 4 (2001), no. 1, 93-118
  13. S.-M. Jung, On the Hyers-Ulam stability of the functional equations that have the quadratic property, J. Math. Anal. Appl. 222 (1998), no. 1, 126-137 https://doi.org/10.1006/jmaa.1998.5916
  14. Y.-S. Jung and K.-H. Park, On the stability of the functional equation f(x + y + xy) =f(x) + f(y) + xf(y) + yf(x), J. Math. Anal. Appl. 274 (2002), no. 2, 659-666 https://doi.org/10.1016/S0022-247X(02)00328-1
  15. H.-M. Kim and I.-S. Chang, Stability of the functional equations related to a multiplicative derivation, J. Appl. &. Computing (series A) 11 (2003), 413-421
  16. Zs. Pales, Remark 27, In 'Report on the 34th ISFE, Aequationes Math' 53 (1997), 200-201
  17. 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
  18. Th. M. Rassias, On the stability of functional equations in Banach spaces, J. Math. Anal. Appl. 251 (2000), no. 1, 264-284 https://doi.org/10.1006/jmaa.2000.7046
  19. Th. M. Rassias, On the stability of functional equations and a problem of Ulam, Acta Appl. Math. 62 (2000), no. 1, 23-130 https://doi.org/10.1023/A:1006499223572
  20. Th. M. Rassias, Functional equations and Inequalities, Mathematics and its Applications, 518. Kluwer Academic Publishers, Dordrecht, 2000
  21. Th. M. Rassias and P. .Semrl, On the behavior of mappings which do not satisfy HyersUlam stability, Proc. Amer. Math. Soc. 114 (1992), no. 4, 989-993 https://doi.org/10.1090/S0002-9939-1992-1059634-1
  22. Th. M. Rassias and J. Tabor, Stability of mapping of Hyers-Ulam Type, Hadronic Press Collection of Original Articles. Hadronic Press, Inc., Palm Harbor, FL, 1994
  23. Th. M. Rassias and J. Tabor, What is left of Hyers-Ulam stability?, J. Natur. Geom. 1 (1992), no. 2, 65-69
  24. P. .Semrl, The functional equation of multiplicative derivation is superstable on standard operator algebras, Integral Equations Operator Theory 18 (1994), no. 1, 118-122 https://doi.org/10.1007/BF01225216
  25. J. Tabor, Remark 20, In `Report on the 34th ISFE, Aequationes Math. 53 (1997), 194-196
  26. S. M. Ulam, Problems in Modern Mathematics, Science Editions John Wiley & Sons, Inc., New York 1964

Cited by

  1. Nearly Quadratic n-Derivations on Non-Archimedean Banach Algebras vol.2012, 2012, https://doi.org/10.1155/2012/961642
  2. APPROXIMATE BI-HOMOMORPHISMS AND BI-DERIVATIONS IN C*-TERNARY ALGEBRAS vol.47, pp.1, 2010, https://doi.org/10.4134/BKMS.2010.47.1.195
  3. CHARACTERIZATIONS OF REAL HYPERSURFACES OF TYPE A IN A COMPLEX SPACE FORM vol.47, pp.1, 2010, https://doi.org/10.4134/BKMS.2010.47.1.001