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Stability of the Jensen functional equation in fuzzy Banach algebras

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In this paper, we prove the Hyers-Ulam stability of the Jensen functional equation in fuzzy Banach algebras by using fixed point method and by using direct method.

Abstract

In this paper, we prove the Hyers-Ulam stability of the Jensen functional equation in fuzzy Banach algebras by using fixed point method and by using direct method.

참고문헌 (51)

  1. R. P. Agarwal, "On Random Topological Structures", Appl. Anal, pp.41~ (2011)[DOI]
  2. T. Aoki, "On the stability of the linear transformation in Banach spaces, On the stability of the linear transformation in Banach spaces", J. Math. Soc. Japan, 2, pp.64~66 (1950)
  3. T. Bag, "Finite dimensional fuzzy normed linear spaces", J. Fuzzy Math, 11, pp.687~705 (2003)
  4. T. Bag, "Fuzzy bounded linear operators", Fuzzy Sets and Systems, 151, pp.513~547 (2005)
  5. Y. J. Cho, "Solutions and Stability of Gener- alized Mixed Type QC Functional Equations in Random Normed Spaces", Inequal. Appl, pp.16~ (2010)
  6. Y. J. Cho, "Fuzzy Functional Inequalities", J. Comput. Anal. Appl, 13, pp.305~320 (2011)
  7. Y. J. Cho, "Lattice Non-Archimedean Random Stability of ACQ Functional Equation", Advan. in Diff. Equat, pp.31~ (2011)
  8. L. Cadariu, "Fixed points and the stability of Jensen's functional equation", J. Inequal. Pure Appl. Math, 4(1), pp.4~ (2003)
  9. L. Cadariu, "On the stability of the Cauchy functional equation: a xed point approach", Grazer Math. Ber, 346, pp.43~52 (2004)
  10. L. Cadariu, "Fixed point methods for the generalized stability of functional equations in a single variable", Fixed Point Theory and Applications 2008 (2008)
  11. S.C. Cheng, "Fuzzy linear operators and fuzzy normed linear spaces", Bull. Calcutta Math. Soc, 86, pp.429~436 (1994)
  12. Y. Cho, "Functional inequalities in non-Archimedean Banach spaces", APPLIED MATHEMATICS LETTERS, 23(0), pp.1238~1242, PERGAMON-ELSEVIER SCIENCE LTD
  13. P.W. Cholewa, "Remarks on the stability of functional equations", Aequationes Math, 27, pp.76~86 (1984)
  14. S. Czerwik, "On the stability of the quadratic mapping in normed spaces", Abh. Math. Sem. Univ. Hamburg, 62, pp.59~64 (1992)
  15. S. Czerwik, "The stability of the quadratic functional equation, In Stability of mappings of Hyers-Ulam type", pp.81~91 (1994), Hadronic Press
  16. P. Czerwik, "Functional Equations and Inequalities in Several Variables" (2002), World Scientific Publishing Company
  17. J. Diaz, "A xed point theorem of the alternative for contractions on a generalized complete metric space", Bull. Amer. Math. Soc, 74, pp.305~309 (1968)
  18. 조열제, "SUBADDITIVITY OF SOME FUNCTIONALS ASSOCIATED TO JENSEN`S INEQUALITY WITH APPLICATIONS", TAIWANESE JOURNAL OF MATHEMATICS, 15(4), pp.1815~1828, MATHEMATICAL SOC REP CHINA
  19. C. Felbin, "Finite dimensional fuzzy normed linear spaces", Fuzzy Sets and Systems, 48, pp.239~248 (1992)
  20. P. Gavruta, "A generalization of the Hyers-Ulam-Rassias stability of approxi- mately additive mappings", J. Math. Anal. Appl, 184, pp.431~436 (1994)
  21. D.H. Hyers, "On the stability of the linear functional equation", Proc. Nat. Acad. Sci. U.S.A, 27, pp.222~224 (1941)
  22. D.H. Hyers, "Stability of Functional Equations in Several Variables" (1998), Birkhauser
  23. G. Isac, "Stability of -additive mappings: Appications to nonlinear analysis", Internat. J. Math. Math. Sci, 19, pp.219~228 (1996)
  24. 정순모, "Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis" (2001), Hadronic Press, Inc.
  25. A.K. Katsaras, "Fuzzy topological vector spaces II", Fuzzy Sets and Systems, 12, pp.143~154 (1984)
  26. I. Kramosil, "Fuzzy metric and statistical metric spaces", Kybernetica, 11, pp.326~334 (1975)
  27. S.V. Krishna, "Separation of fuzzy normed linear spaces", Fuzzy Sets and Systems, 63, pp.207~217 (1994)
  28. D. Mihet, "On the stability of the additive Cauchy functional equa- tion in random normed spaces", J. Math. Anal. Appl, 343, pp.567~572 (2008)
  29. M. Mirzavaziri, "A xed point approach to stability of a quadratic equation", Bull. Braz. Math. Soc, 37, pp.361~376 (2006)
  30. A.K. Mirmostafaee, "Fuzzy stability of the Jensen functional equation", Fuzzy Sets and Systems, 159, pp.730~738 (2008)
  31. A.K. Mirmostafaee, "Fuzzy versions of Hyers-Ulam-Rassias theorem", Fuzzy Sets and Systems, 159, pp.720~729 (2008)
  32. A.K. Mirmostafaee, "Fuzzy approximately cubic mappings", Inform. Sci, 178, pp.3791~3798 (2008)
  33. M. Mohammadi, "Random Stabil- ity of an Additive-quadratic-quartic Functional Equation", J. Inequal. Appl, pp.18~ (2010)
  34. A. Najati, "Generalized Hyers{Ulam Stability of the Pexiderized Cauchy Functional Equation in Non-Archimedean Spaces", Fixed Point Theory Appl, pp.11~ (2011)[DOI]
  35. A. Najati, "Local Stability of the Pexiderized Cauchy and Jensen's equations in Fuzzy Spaces", J. Inequal. Appl (2011)[DOI]
  36. C. Park, "Fixed points and Hyers-Ulam-Rassias stability of Cauchy-Jensen func- tional equations in Banach algebras", Fixed Point Theory and Applications (2007)
  37. C. Park, "Generalized Hyers-Ulam-Rassias stability of quadratic functional equa- tions: a xed point approach", Fixed Point Theory and Applications 2008 (2008)
  38. V. Radu, "The xed point alternative and the stability of functional equations", Fixed Point Theory, 4, pp.91~96 (2003)
  39. Th.M. Rassias, "On the stability of the linear mapping in Banach spaces", Proc. Amer. Math. Soc, 72, pp.297~300 (1978)
  40. Th.M. Rassias, "Problem 16; 2, Report of the 27th International Symp. on Functional Equations", Aequationes Math, 39, pp.292~293 (1990)
  41. Th.M. Rassias, "On the stability of the quadratic functional equation and its ap- plications", Studia Univ. Babes-Bolyai XLIII, pp.89~124 (1998)
  42. Th.M. Rassias, "The problem of S.M. Ulam for approximately multiplicative map- pings", J. Math. Anal. Appl, 246, pp.352~378 (2000)
  43. Th.M. Rassias, "On the stability of functional equations in Banach spaces", J. Math. Anal. Appl, 251, pp.264~284 (2000)
  44. Th.M. Rassias, "On the stability of functional equations and a problem of Ulam", Acta Appl. Math, 62, pp.23~130 (2000)
  45. Th.M. Rassias, "On the behaviour of mappings which do not satisfy Hyers-Ulam stability", Proc. Amer. Math. Soc, 114, pp.989~993 (1992)
  46. Th.M. Rassias, "On the Hyers-Ulam stability of linear mappings", J. Math. Anal. Appl, 173, pp.325~338 (1993)
  47. Th.M. Rassias, "Variational problem of some quadratic function- als in complex analysis", J. Math. Anal. Appl, 228, pp.234~253 (1998)
  48. R. Saadati, "Non-Archimedean L-fuzzy normed spaces and stability of functional equations", Computers Math. Appl, 60, pp.2488~2496 (2010)
  49. F. Skof, "Proprieta locali e approssimazione di operatori", Rend. Sem. Mat. Fis. Milano, 53, pp.113~129 (1983)
  50. S. M. Ulam, "A Collection of the Mathematical Problems" (1960), Interscience Publ
  51. J.Z. Xiao, "Fuzzy normed spaces of operators and its completeness", Fuzzy Sets and Systems, 133, pp.389~399 (2003)

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