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On the Stability of Jordan *-Derivation Pairs

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Abstract

In this article, the Hyers–Ulam stability of Jordan *-derivation pairs for the Cauchy additive functional equation and the Cauchy additive functional inequality is proved. A fixed point method to establish of the stability and the superstability for Jordan *-derivation pairs is also employed.

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References

  1. Alimohammady M., Sadeghi A.: Some new results on the superstability of the Cauchy equation on semigroups. Results Math. 63, 705–712 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  2. Almira J.M.: A note on classical and p-adic Fréchet functional equations with restrictions. Results Math. 63, 649–656 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  3. Aoki T.: On the stability of the linear transformation in Banach spaces. J. Math. Soc. Jpn. 2, 64–66 (1950)

    Article  MATH  Google Scholar 

  4. Bodaghi, A., Alias, I.A., Ghahramani, M.H.: Approximately cubic functional equations and cubic multipliers. J. Inequal. Appl. 2011, 9 (2011) (Article No.: 53)

  5. Bodaghi, A., Alias, I.A., Ghahramani, M.H.: Ulam stability of a quartic functional equation. Abstr. Appl. Anal. 2012, 9 (2012) (Article ID: 232630)

  6. Bodaghi A., Eshaghi Gordji M., Paykan K.: Approximate multipliers and approximate double centralizers: a fixed point approach. An. St. Univ. Ovidius Constanta 20(3), 21–32 (2012)

    MathSciNet  MATH  Google Scholar 

  7. Bratteli, O.: Derivation, Dissipation and Group Actions on C*-Algebras. In: Lecture Notes in Mathematics, vol. 1229. Springer, Berlin (1986)

  8. Bratteli O., Goodman F.M., Jørgensen P.E.T.: Unbouded derivations tangential to compact groups of automorphisms II. J. Funct. Anal. 61, 247–289 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  9. Cădariu L., Radu V.: Fixed points and the stability of quadratic functional equations. An. Univ. Timisoara Ser. Mat. Inform. 41, 25–48 (2003)

    MATH  Google Scholar 

  10. Cădariu L., Radu V.: On the stability of the Cauchy functional equation: A fixed point approach. Grazer Math. Ber. 346, 43–52 (2004)

    MATH  Google Scholar 

  11. Chang I., Eshaghi Gordji M., Khodaei H., Kim H.: Nearly quartic mappings in β-homogeneous F-spaces. Results Math. 63, 529–541 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  12. Diaz J.B., Margolis B.: A fixed point theorem of the alternative for contractions on a generalized complete metric space. Bull. Am. Math. Soc. 74, 305–309 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  13. Ebadian A., Ghobadipour H.: A fixed point approach to almost double derivations and Lie *-double drivations. Results Math. 63, 409–423 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  14. Eshaghi Gordji M., Bodaghi A., Park C.: A fixed point approach to the stability of double Jordan centralizers and Jordan multipliers on Banach algebras. U.P.B. Sci. Bull. Ser. A 73(2), 65–73 (2011)

    MathSciNet  MATH  Google Scholar 

  15. Fechner W.: Stability of a functional inequalities associated with the Jordan–von Neumann functional equation. Aequationes Math. 71, 149–161 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  16. Gǎvruta P.: A generalization of the Hyers–Ulam–Rassias stability of approximately additive mappings. J. Math. Anal. Appl. 184, 431–436 (1994)

    Article  MathSciNet  Google Scholar 

  17. Gilányi A.: Eine zur Parallelogrammgleichung äquivalente Ungleichung. Aequationes Math. 62, 303–309 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  18. Gilányi, A.: (2002) On a problem by K. Nikodem. Math. Inequal. Appl. 5: 707–710

    Google Scholar 

  19. Hyers D.H.: On the stability of the linear functional equation. Proc. Natl. Acad. Sci. USA 27, 222–224 (1941)

    Article  MathSciNet  Google Scholar 

  20. Lee S., Jang S.: Unbounded derivations on compact actions of C*-algebras. Commun. Korean Math. Soc. 5, 79–86 (1990)

    Google Scholar 

  21. Monlar L.: Jordan *-derivation pairs on a complex *-algebra. Aequationes Math. 54, 44–55 (1997)

    Article  MathSciNet  Google Scholar 

  22. Moslehian M.S., Rahbarnia F., Sahoo P.K.: Approximate double centralizers are exact double centralizers. Bol. Soc. Mat. Mex. 13, 111–122 (2007)

    MathSciNet  MATH  Google Scholar 

  23. Park, C.: Isomorphisms between C*-ternary algebras. J. Math. Phys. 47,12 (2006) (Article ID: 103512)

    Google Scholar 

  24. Park, C., Bodaghi, A.: On the stability of *-derivations on Banach *-algebras. Adv. Differ. Equ. 2012, 10 (2012) (Article No.: 138)

  25. Park, C., Cho, Y., Han, M.: Functional inequalities associated with Jordan–von Neumann-type additive functional equations. J. Inequal. Appl. 2007, 13 (2007) (Article ID: 41820)

  26. Rassias Th.M.: On the stability of the linear mapping in Banach spaces. Proc. Am. Math. Soc. 72, 297–300 (1978)

    Article  MATH  Google Scholar 

  27. Rätz J.: On inequalities associated with the Jordan–von Neumann functional equation. Aequationes Math. 66, 191–200 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  28. Ulam S.M.: Problems in Modern Mathematics, Chapter VI, Science ed. Wiley, New York (1940)

    Google Scholar 

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Correspondence to Abasalt Bodaghi.

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Bodaghi, A., Jang, S.Y. & Park, C. On the Stability of Jordan *-Derivation Pairs. Results. Math. 64, 289–303 (2013). https://doi.org/10.1007/s00025-013-0314-x

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