The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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LIE BRACKET JORDAN DERIVATIONS IN BANACH JORDAN ALGEBRAS

  • Paokanta, Siriluk (Department of Mathematics, Research Institute for Natural Sciences, Hanyang University) ;
  • Lee, Jung Rye (Department of Mathematics, Daejin University)
  • Received : 2019.09.30
  • Accepted : 2021.01.10
  • Published : 2021.05.31
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Abstract

In this paper, we introduce Lie bracket Jordan derivations in Banach Jordan algebras. Using the direct method and the fixed point method, we prove the Hyers-Ulam stability of Lie bracket Jordan derivations in complex Banach Jordan algebras.

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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. L. Cadariu, V. Radu, Fixed points and the stability of Jensen's functional equation, J. Inequal. Pure Appl. Math. 4, no. 1, Art. ID 4 (2003).
  3. L. Cadariu & V. Radu: On the stability of the Cauchy functional equation: a fixed point approach. Grazer Math. Ber. 346 (2004), 43-52.
  4. L. Cadariu & V. Radu: Fixed point methods for the generalized stability of functional equations in a single variable. Fixed Point Theory Appl. 2008, Art. ID 749392 (2008).
  5. P.W. Cholewa: Remarks on the stability of functional equations. Aequationes Math. 27 (1984), 76-86. https://doi.org/10.1007/BF02192660
  6. J. Diaz & B. Margolis: A fixed point theorem of the alternative for contractions on a generalized complete metric space. Bull. Am. Math. Soc. 74 (1968), 305-309. https://doi.org/10.1090/S0002-9904-1968-11933-0
  7. N. Eghbali, J.M. Rassias & M. Taheri: On the stability of a k-cubic functional equation in intuitionistic fuzzy n-normed spaces. Results Math. 70 (2016), 233-248. https://doi.org/10.1007/s00025-015-0476-9
  8. Iz. EL-Fassi: Solution and approximation of radical quintic functional equation related to quintic mapping in quasi-β-Banach spaces. Rev. R. Acad. Cienc. Exactas F'is. Nat. Ser. A Mat. 113 (2019), no. 2, 675-687. https://doi.org/10.1007/s13398-018-0506-z
  9. 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
  10. D.H. Hyers: On the stability of the linear functional equation. Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222-224. https://doi.org/10.1073/pnas.27.4.222
  11. G. Isac & Th.M. Rassias: Stability of ψ-additive mappings: Applications to nonlinear analysis. Int. J. Math. Math. Sci. 19 (1996), 219-228. https://doi.org/10.1155/S0161171296000324
  12. D. Mihet, & V. Radu: On the stability of the additive Cauchy functional equation in random normed spaces. J. Math. Anal. Appl. 343 (2008), 567-572. https://doi.org/10.1016/j.jmaa.2008.01.100
  13. C. Park: Homomorphisms between Poisson JC*-algebras. Bull. Braz. Math. Soc. 36 (2005), 79-97. https://doi.org/10.1007/s00574-005-0029-z
  14. C. Park: Additive ρ-functional inequalities and equations. J. Math. Inequal. 9 (2015), 17-26. https://doi.org/10.7153/jmi-09-02
  15. C. Park: Additive ρ-functional inequalities in non-Archimedean normed spaces. J. Math. Inequal. 9 (2015), 397-407. https://doi.org/10.7153/jmi-09-33
  16. C. Park: Fixed point method for set-valued functional equations. J. Fixed Point Theory Appl. 19 (2017), 2297-2308. https://doi.org/10.1007/s11784-017-0418-0
  17. C. Park: Set-valued additive ρ-functional inequalities. J. Fixed Point Theory Appl. 20 (2018), no. 2, 20:70.
  18. V. Radu: The fixed point alternative and the stability of functional equations. Fixed Point Theory 4 (2003), 91-96.
  19. Th.M. Rassias: On the stability of the linear mapping in Banach spaces. Proc. Am. Math. Soc. 72 (1978), 297-300. https://doi.org/10.1090/S0002-9939-1978-0507327-1
  20. F. Skof: Propriet locali e approssimazione di operatori. Rend. Sem. Mat. Fis. Milano 53 (1983), 113-129. https://doi.org/10.1007/BF02924890
  21. L. Sz'ekelyhidi: Superstability of functional equations related to spherical functions, Open Math. 15 (2017), no. 1, 427-432. https://doi.org/10.1515/math-2017-0038
  22. S.M. Ulam: A Collection of the Mathematical Problems. Interscience Publ. New York, 1960.
  23. Z. Wang: Stability of two types of cubic fuzzy set-valued functional equations. Results Math. 70 (2016), 1-14. https://doi.org/10.1007/s00025-015-0457-z