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Fixed points and stability of an AQCQ-functional equation in $G$-normed spaces

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In this paper, we introduce functional equations in $G$-normed spaces and we prove the Hyers-Ulam stability of an additive-quadratic-cubic-quartic functional equation in complete $G$-normed spaces by using the fixed point method.

Abstract

In this paper, we introduce functional equations in $G$-normed spaces and we prove the Hyers-Ulam stability of an additive-quadratic-cubic-quartic functional equation in complete $G$-normed spaces by using the fixed point method.

참고문헌 (44)

  1. J. Aczel, "Functional Equations in Several Variables" (1989), Cambridge Univ. Press
  2. T. Aoki, "On the stability of the linear transformation in Banach spaces", J. Math. Soc. Japan, 2, pp.64~66 (1950)
  3. D.G. Bourgin, "Classes of transformations and bordering transformations", Bull. Amer. Math. Soc, 57, pp.223~237 (1951)
  4. L. C. adariu, "Fixed points and the stability of Jensen's functional equation", J. Inequal. Pure Appl. Math, 4(1) (2003)
  5. L. C. adariu, "On the stability of the Cauchy functional equation: a ¯xed point approach", Grazer Math. Ber, 346, pp.43~52 (2004)
  6. L. C. adariu, "Fixed point methods for the generalized stability of functional equations in a single variable", Fixed Point Theory and Applications (2008)
  7. Y. Cho, "Functional inequalities in non-Archimedean Banach spaces", Appl. Math. Letters, 23, pp.1238~1242 (2010)
  8. P.W. Cholewa, "Remarks on the stability of functional equations", Aequationes Math, 27, pp.76~86 (1984)
  9. C.-Y. Chou, "On approximate isomorphisms between Banach *-algebras or C¤-algebras", Taiwanese J. Math, 10, pp.219~231 (2006)
  10. S. Czerwik, "On the stability of the quadratic mapping in normed spaces", Abh. Math. Sem. Univ. Hamburg, 62, pp.59~64 (1992)
  11. P. Czerwik, "Functional Equations and Inequalities in Several Variables" (2002), World Scientic Publishing Company
  12. 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)
  13. M. Eshaghi Gordji, "On the stability of a generalized qua-dratic and quartic type functional equation in quasi-Banach spaces", J. Inequal. Appl (2009)
  14. M. Eshaghi Gordji, "Stability of an additive-cubic-quartic functional equation", Advances in Di®erence Equations (2009)
  15. G.L. Forti, "Comments on the core of the direct method for proving Hyers-Ulam stability of functional equations", J. Math. Anal. Appl, 295, pp.127~133 (2004)
  16. G.L. Forti, "Elementary remarks on Ulam-Hyers stability of linear functional equations", J. Math. Anal. Appl, 328, pp.109~118 (2007)
  17. P. Gavruta, "A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings", J. Math. Anal. Appl, 184, pp.431~436 (1994)
  18. D.H. Hyers, "On the stability of the linear functional equation", Proc. Nat. Acad. Sci. U.S.A, 27, pp.222~224 (1941)
  19. D.H. Hyers, "Stability of Functional Equations in Several Variables" (1998), BirkhÄauser
  20. G. Isac, "Stability of Ã-additive mappings: Appications to nonlinear analysis", Internat. J. Math. Math. Sci, 19, pp.219~228 (1996)
  21. K. Jun, "The generalized Hyers-Ulam-Rassias stability of a cubic functional equation", J. Math. Anal. Appl, 274, pp.867~878 (2002)
  22. K. Jun, "Approximate derivations mapping into the radicals of Banach algebras", Tai-wanese J. Math, 11, pp.277~288 (2007)
  23. S. Jung, "Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Anal-ysis" (2001), Hadronic Press lnc
  24. J. Lee, "A xed point approach to the stability of an additive-quadratic-cubic-quartic functional equation", Fixed Point Theory and Applications (2010)
  25. S. Lee, "Quartic functional equations", J. Math. Anal. Appl, 307, pp.387~394 (2005)
  26. D. Mihet, "On the stability of the additive Cauchy functional equation in random normed spaces", J. Math. Anal. Appl, 343, pp.567~572 (2008)
  27. M. Mirzavaziri, "A xed point approach to stability of a quadratic equation", Bull. Braz. Math. Soc, 37, pp.361~376 (2006)
  28. M.S. Moslehian, "Jensen's functional equations in multi-normed spaces", Taiwanese J. Math, 14, pp.453~462 (2010)
  29. Z. Mustafa, "A new approach to generalized metric spaces", J. Nonlinear Convex Anal, 7, pp.289~297 (2006)
  30. C. Park, "Linear functional equations in Banach modules over a C¤-algebra", Acta Appl. Math, 77, pp.125~161 (2003)
  31. C. Park, "Fixed points and Hyers-Ulam-Rassias stability of Cauchy-Jensen functional equations in Banach algebras", Fixed Point Theory and Applications (2007)
  32. C. Park, "Generalized Hyers-Ulam-Rassias stability of quadratic functional equations:a xed point approach", Fixed Point Theory and Applications (2008)
  33. C. Park, "Fixed points and the stability of an AQCQ-functional equation in non-Archimedean normed spaces", Abstract and Applied Analysis (2010)
  34. 박춘길, "ON THE STABILITY OF AN AQCQ-FUNCTIONAL EQUATION", 충청수학회지, 22(4), pp.757~770 (2009), 충청수학회
  35. C. Park, "Hyers-Ulam stability of functional equations in G-normed spaces", ~
  36. V. Radu, "The xed point alternative and the stability of functional equations", Fixed Point Theory, 4, pp.91~96 (2003)
  37. M. Rassias, "On the stability of the linear mapping in Banach spaces", Proc. Amer. Math. Soc, 72, pp.297~300 (1978)
  38. M. Rassias, "On the stability of functional equations in Banach spaces", J. Math. Anal. Appl, 251, pp.264~284 (2000)
  39. M. Rassias, "On the stability of functional equations and a problem of Ulam", Acta Appl. Math, 62, pp.23~130 (2000)
  40. M. Rassias, "On the behaviour of mappings which do not satisfy Hyers-Ulam stability", Proc. Amer. Math. Soc, 114, pp.989~993 (1992)
  41. M. Rassias, "On the Hyers-Ulam stability of linear mappings", J. Math. Anal. Appl, 173, pp.325~338 (1993)
  42. R. Saadati, "Non-Archimedean L-fuzzy normed spaces and stability of func-tional equations", Computers Math. Appl, 60, pp.2488~2496 (2010)
  43. F. Skof, "Proprietµa locali e approssimazione di operatori", Rend. Sem. Mat. Fis. Milano, 53, pp.113~129 (1983)
  44. S.M. Ulam, "A Collection of the Mathematical Problems" (1960), Interscience Publ

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