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Fuzzy stability of a cubic-quartic functional equation: a fixed point approach

신동윤|박춘길|장선영
대한수학회 (The Korean Mathematical Society)|2011.05|대한수학회보 (Bulletin of the KMS)|제48권 제3호|pp. 491-503

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참고문헌

키워드

fixed pointfuzzy Banach spacegeneralized Hyers-Ulam stabilitycubic mappingquartic mapping
주제분류수학

초록

Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following cubic-quartic functional equation (0. 1)f(2x+y) + f(2x-y) = 3f(x+y) + f(-x-y) + 3 f(x-y) + f(y-x) + 18f(x) + 6f(-x) - 3f(y) - 3f(-y) in fuzzy Banach spaces.

Abstract

Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following cubic-quartic functional equation (0. 1)f(2x+y) + f(2x-y) = 3f(x+y) + f(-x-y) + 3 f(x-y) + f(y-x) + 18f(x) + 6f(-x) - 3f(y) - 3f(-y) in fuzzy Banach spaces.

참고문헌 (37)

  1. T. Aoki, "On the stability of the linear transformation in Banach spaces", J. Math. Soc. Japan, 2, pp.64~66 (1950)
  2. T. Bag, "Finite dimensional fuzzy normed linear spaces", J. Fuzzy Math, 11(3), pp.687~705 (2003)
  3. T. Bag, "Fuzzy bounded linear operators", Fuzzy Sets and Systems, 151(3), pp.513~547 (2005)
  4. L. Cadariu, "Fixed points and the stability of Jensen's functional equation", J. Inequal. Pure Appl. Math, 4(1) (2003)
  5. L. Cadariu, "On the stability of the Cauchy functional equation: a fixed point approach", Iteration theory (ECIT '02), 통권 : 346, pp.43~52 (2004), Karl-Franzens-Univ
  6. L. Cadariu, "Fixed point methods for the generalized stability of functional equations in a single variable", Fixed Point Theory and Applications 2008 (2008)
  7. S. C. Cheng, "Fuzzy linear operators and fuzzy normed linear spaces", Bull. Calcutta Math. Soc, 86(5), pp.429~436 (1994)
  8. P. W. Cholewa, "Remarks on the stability of functional equations", Aequationes Math, 27(1), pp.76~86 (1984)
  9. S. Czerwik, "On the stability of the quadratic mapping in normed spaces", Abh. Math. Sem. Univ. Hamburg, 62, pp.59~64 (1992)
  10. J. Diaz, "A fixed point theorem of the alternative for contractions on a generalized complete metric space", Bull. Amer. Math. Soc, 74, pp.305~309 (1968)
  11. C. Felbin, "Finite dimensional fuzzy normed linear spaces", Fuzzy Sets and Systems, 48(2), pp.239~248 (1992)
  12. P. Gavruta, "A generalization of the Hyers-Ulam-Rassias stability of approximately ad- ditive mappings", J. Math. Anal. Appl, 184(3), pp.431~436 (1994)
  13. D. H. Hyers, "On the stability of the linear functional equation", Proc. Nat. Acad. Sci. U.S.A, 통권 : 27, pp.222~224 (1941)
  14. D. H. Hyers, "Stability of Functional Equations in Several Variables" (1998), Birkhauser
  15. G. Isac, "Stability of -additive mappings: Appications to nonlinear analysis", Internat. J. Math. Math. Sci, 19(2), pp.219~228 (1996)
  16. K. Jun, "The generalized Hyers-Ulam-Rassias stability of a cubic functional equation", J. Math. Anal. Appl, 274(2), pp.267~278 (2002)
  17. 정순모, "Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis" (2001), Hadronic Press, Inc.
  18. A. K. Katsaras, "Fuzzy topological vector spaces II", Fuzzy Sets and Systems, 12(2), pp.143~154 (1984)
  19. I. Kramosil, "Fuzzy metric and statistical metric spaces", Kybernetica, 11(5), pp.336~344 (1975)
  20. S. V. Krishna, "Separation of fuzzy normed linear spaces", Fuzzy Sets and Systems, 63(2), pp.207~217 (1994)
  21. S. Lee, "Quartic functional equations", J. Math. Anal. Appl, 307(2), pp.387~394 (2005)
  22. D. Mihet, "On the stability of the additive Cauchy functional equation in random normed spaces", J. Math. Anal. Appl, 343(1), pp.567~572 (2008)
  23. M. Mirzavaziri, "A fixed point approach to stability of a quadratic equation", Bull. Braz. Math. Soc, 37(3), pp.361~376 (2006)
  24. A. K. Mirmostafaee, "Fuzzy stability of the Jensen functional equation", Fuzzy Sets and Systems, 159(6), pp.730~738 (2008)
  25. A. K. Mirmostafaee, "Fuzzy versions of Hyers-Ulam-Rassias theo- rem", Fuzzy Sets and Systems, 159(6), pp.720~729 (2008)
  26. A. K. Mirmostafaee, "Fuzzy approximately cubic mappings", Inform. Sci, 178(19), pp.3791~3798 (2008)
  27. C. Park, "Fixed points and Hyers-Ulam-Rassias stability of Cauchy-Jensen functional equations in Banach algebras", Fixed Point Theory Appl (2007)
  28. C. Park, "Generalized Hyers-Ulam stability of quadratic functional equations: a fixed point approach", Fixed Point Theory Appl (2008)
  29. C. Park, "Functional inequalities associated with Jordan-von Neu- mann type additive functional equations", J. Inequal. Appl (2007)
  30. C. Park, "Generalized stability of C*-ternary quadratic mappings", Abstr. Appl. Anal (2007)
  31. C. Park, "Homomorphisms and derivations in C*-algebras", Abstr. Appl. Anal (2007)
  32. V. Radu, "The fixed point alternative and the stability of functional equations", Fixed Point Theory, 4(1), pp.91~96 (2003)
  33. Th. M. Rassias, "On the stability of the linear mapping in Banach spaces", Proc. Amer. Math. Soc, 72(2), pp.297~300 (1978)
  34. Th. M. Rassias, "On the stability of functional equations and a problem of Ulam", Acta Appl. Math, 62(1), pp.23~130 (2000)
  35. F. Skof, "Local properties and approximation of operators", Rend. Sem. Mat. Fis. Milano, 53, pp.113~129 (1983)
  36. S. M. Ulam, "A Collection of the Mathematical Problems" (1960), Interscience Publ
  37. J. Z. Xiao, "Fuzzy normed spaces of operators and its completeness", Fuzzy Sets and Systems, 133(3), pp.389~399 (2003)

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