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APPROXIMATELY QUINTIC AND SEXTIC MAPPINGS ON THE PROBABILISTIC NORMED SPACES

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주제분류수학

초록

We prove the stability for the systems of quadratic-cubic and additive-quadratic-cubic functional equations with constant coefficients on the probabilistic normed spaces (briefly PN spaces).

Abstract

We prove the stability for the systems of quadratic-cubic and additive-quadratic-cubic functional equations with constant coefficients on the probabilistic normed spaces (briefly PN spaces).

참고문헌 (80)

  1. J. Aczel, "Functional Equations in Several Variables" (1989), Cambridge Uni- versity Press
  2. C. Alsina, "On the definition of a probabilistic normed space", Aequationes Math, 46(1), pp.91~98 (1993)
  3. T. Aoki, "On the stability of the linear transformation in Banach spaces", J. Math. Soc. Japan, 2, pp.64~66 (1950)
  4. P. W. Cholewa, "Remarks on the stability of functional equations", Aequationes Math, 27(1), pp.76~86 (1984)
  5. Jukang K. Chung, "On the general solution of a quartic functional equation", 대한수학회보, 40(4), pp.565~576 (2003), 대한수학회
  6. S. Czerwik, "On the stability of the quadratic mapping in normed spaces", Abh. Math. Sem. Univ. Hamburg, 62, pp.59~64 (1992)
  7. S. Czerwik, "Functional Equations and Inequalities in Several Variables" (2002), World Scientific
  8. A. Ebadian, "A fixed point method for perturbation of bimultipliers and Jordan bimultipliers in C*-ternary algebras", J. Math. Phys, 51(1), pp.10~ (2010)[DOI]
  9. A. Ebadian, "On approximate additive-quartic and quadratic-cubic functional equations in two variables on abelian groups", Results Math, 58(1), pp.39~53 (2010)
  10. Madjid Eshaghi Gordji, "STABILITY OF A FUNCTIONAL EQUATION DERIVING FROM QUARTIC AND ADDITIVE FUNCTIONS", 대한수학회보, 47(3), pp.491~502 (2010), 대한수학회
  11. M. Eshaghi Gordji, "Stability of an additive-quadratic functional equation of two variables in F- spaces", J. Nonlinear Sci. Appl, 2(4), pp.251~259 (2009)
  12. M. Eshaghi Gordji, "On the stability of generalized mixed type quadratic and quartic functional equation in quasi-Banach spaces", J. Ineq. Appl, 2009, pp.26~ (2009)
  13. M. Eshaghi Gordji, "On approximate cubic homomorphisms", Adv. Difference Equ, 2009, pp.11~ (2009)[DOI]
  14. M. Eshaghi Gordji, "Solution and stability of a mixed type cubic and quartic functional equation in quasi-Banach spaces", Abstr. Appl. Anal, 2009, pp.1~14 (2009)
  15. M. Eshaghi Gordji, "Stability of a functional equation deriving from cubic and quartic functions", Abs. Appl. Anal, 2008, pp.17~ (2008)
  16. M. Eshaghi Gordji, "On the stability of J*-derivations", J. Geom. Phys, 60(3), pp.454~459 (2010)
  17. M. Eshaghi Gordji, "Generalized Hyers-Ulam-Rassias Theorem in Menger Probabilistic Normed Spaces", Discrete Dyn. Nat. Soc, 2010, pp.11~ (2010)
  18. M. Eshaghi Gordji, "Generalized Ulam-Hyers stability of Jensen functional equation in Sherstnev PN spaces", J. Inequal. Appl, 2010, pp.14~ (2010)
  19. M. Eshaghi Gordji, "Stability of (α; β; γ)-derivations on Lie C*-algebras", Int. J. Geom. Methods Mod. Phys, 7(7), pp.1093~1102 (2010)
  20. M. Eshaghi Gordji, "Ternary Jordan *-derivations in C*-ternary algebras", J. Comput. Anal. Appl, 12(2), pp.463~470 (2010)
  21. M. Eshaghi Gordji, "Stability of an additive-cubic-quartic functional equation", Adv. Difference Equ, 2009, pp.20~ (2009)
  22. M. Eshaghi Gordji, "Solution and stability of a mixed type additive, quadratic and cubic functional equation", Adv. Difference Equ, 2009, pp.17~ (2009)
  23. M. Eshaghi Gordji, "Approximately n-Jordan homomorphisms on Banach algebras", J. Inequal. Appl, 2009, pp.8~ (2009)
  24. M. Eshaghi Gordji, "Solution and stability of generalized mixed type cubic, quadratic and additive functional equation in quasi-Banach spaces", Nonlinear Anal, 71(11), pp.5629~5643 (2009)
  25. M. Eshaghi Gordji, "On the generalized Hyers-Ulam-Rassias stability of quadratic functional equa- tions", Abstr. Appl. Anal, 2009, pp.11~ (2009)
  26. M. Eshaghi Gordji, "The fixed point method for fuzzy approximation of a functional equation associated with inner product spaces", Discrete Dyn. Nat. Soc, 2010, pp.15~ (2010)[DOI]
  27. M. Eshaghi Gordji, "General quartic-cubic-quadratic functional equation in non-Archimedean normed spaces", Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys, 72(3), pp.69~84 (2010)
  28. M. Eshaghi Gordji, "Approximately J*-homomorphisms: A fixed point approach", J. Geom. Phys, 60(5), pp.809~814 (2010)
  29. M. Eshaghi Gordji, "Generalized Hyers-Ulam sta- bility of the generalized (n; k)-derivations", Abstr. Appl. Anal, 2009, pp.8~ (2009)
  30. M. Eshaghi Gordji, "Approximation of generalized homomorphisms in quasi-Banach algebras", Analele Univ. Ovidius Constata, Math series, 17(2), pp.203~214 (2009)
  31. M. Eshaghi Gordji, "Stability of cubic and quartic functional equations in non-Archimedean spaces", Acta Appl. Math, 110(3), pp.1321~1329 (2010)
  32. M. Eshaghi Gordji, "Stability of mixed type cubic and quartic functional equations in random normed spaces", J. Inequal. Appl, 2009, pp.9~ (2009)
  33. M. Eshaghi Gordji, "Stability of a mixed type cubic-quartic functional equation in non-Archimedean spaces", Appl. Math. Lett, 23(10), pp.1198~1202 (2010)
  34. M. Eshaghi Gordji, "Stability of a mixed type additive and quadratic functional equation in non-Archimedean spaces", J. Comput. Anal. Appl, 12(2), pp.454~462 (2010)
  35. M. Eshaghi Gordji, "Quadratic-quartic functional equa- tions in RN-spaces", J. Inequal. Appl, 2009, pp.14~ (2009)
  36. Z. Gajda, "On stability of additive mappings", Internat. J. Math. Math. Sci, 14(3), pp.431~434 (1991)
  37. 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)
  38. P. Gavruta, "A new method for the generalized Hyers-Ulam-Rassias stability", Int. J. Nonlinear Anal. Appl, 1(2), pp.11~18 (2010)
  39. N. Ghobadipour, "A perturbation of double derivations on Banach algebras", Commun. Math. Anal, 11(1), pp.51~60 (2011)
  40. D. H. Hyers, "On the stability of the linear functional equation", Proc. Nat. Acad. Sci. USA, 27, pp.222~224 (1941)
  41. D. H. Hyers, "Stability of Functional Equations in Several Variables" (1998), Birkhauser
  42. K. W. Jun, "The generalized Hyers-Ulam-Rassias stability of a cubic functional equation", J. Math. Anal. Appl, 274, pp.267~278 (2002)
  43. K. W. Jun, "On the Hyers-Ulam stability of an Euler- Lagrange type cubic functional equation", J. Comput. Anal. Appl, 7(1), pp.21~33 (2005)
  44. 정순모, "Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis" (2001), Hadronic Press, Inc.
  45. S.-M. Jung, "Hyers-Ulam-Rassias stability of Jensen's equation and its application", Proc. Amer. Math. Soc, 126(11), pp.3137~3143 (1998)
  46. S.-M. Jung, "Stability of the quadratic equation of Pexider type", Abh. Math. Sem. Univ. Hamburg, 70, pp.175~190 (2000)
  47. P. Kannappan, "Quadratic functional equation and inner product spaces", Results Math, 27(3), pp.368~372 (1995)
  48. H. Khodaei, "Fuzzy approximately additive mappings", Int. J. Nonlinear Anal. Appl, 1(2), pp.44~53 (2010)
  49. H. Khodaei, "Approximately generalized additive functions in several variables", Int. J. Nonlinear Anal. Appl, 1, pp.22~41 (2010)
  50. S. H. Lee, "Quartic functional equation", J. Math. Anal. Appl, 307(2), pp.387~394 (2005)
  51. Alireza Kamel Mirmostafaee, "Stability of Quartic Mappings in Non-Archimedean Normed Spaces", Kyungpook Mathematical Journal, 49(2), pp.289~297 (2009), 경북대학교 자연과학대학 수학과
  52. A. Najati, "On the stability of a quartic functional equation", J. Math. Anal. Appl, 340(1), pp.569~574 (2008)
  53. Abbas Najati, "Hyers-Ulam-Rassias Stability of a Cubic Functional Equation", 대한수학회보, 44(4), pp.825~840 (2007), 대한수학회
  54. A. Najati, "Stability of an Euler-Lagrange type cubic functional equa- tion", Turkish J. Math, 33(1), pp.65~73 (2009)
  55. A. Najati, "Stability of a mixed additive, quadratic and cubic functional equation in quasi- Banach spaces", Aust. J. Math. Anal. Appl, 5(2), pp.10~21 (2008)
  56. A. Najati, "Stability of a mixed additive and cubic functional equation in quasi-Banach spaces", J. Math. Anal. Appl, 342(2), pp.1318~1331 (2008)
  57. A. Najati, "On the stability of a cubic functional equation", Acta Math. Sin.(Engl. Ser.), 24(12), pp.1953~1964 (2008)
  58. C. Park, "On an approximate automorphism on a C*-algebra", Proc. Amer. Math. Soc, 132(6), pp.1739~1745 (2004)
  59. C. Park, "On the stability of the orthogonally quartic functional equation", Bull. Iranian Math. Soc, 31(1), pp.63~70 (2005)
  60. "J. Math. Phys", 2010, 044102~
  61. C. Park, "Generalized additive functional inequalities in Banach algebras", Int. J. Nonlinear Anal. Appl, 1(2), pp.54~62 (2010)
  62. C. Park, "Stability of the Jensen-type functional equation in C*- algebras: A Fixed Point Approach", Abstr. Appl. Anal, 2009, pp.1~17 (2009)[DOI]
  63. C. Park, "Isomorphisms in unital C*-algebras", Int. J. Nonlinear Anal. Appl, 1(2), pp.1~10 (2010)
  64. J. M. Rassias, "On approximation of approximately linear mappings by linear mappings", J. Funct. Anal, 46(1), pp.126~130 (1982)
  65. J. M. Rassias, "On Approximation of approximately linear mappings by linear mappings", Bull. Sci. Math. (2), 108(4), pp.445~446 (1984)
  66. J. M. Rassias, "On a new approximation of approximately linear mappings by linear mappings", Discuss. Math, 7, pp.193~196 (1985)
  67. J. M. Rassias, "Solution of a problem of Ulam", J. Approx. Theory, 57(3), pp.268~273 (1989)
  68. J. M. Rassias, "On the stability of the Euler-Lagrange functional equation", Chinese J. Math, 20(2), pp.185~190 (1992)
  69. J. M. Rassias, "Solution of a stability problem of Ulam", Discuss. Math, 12, pp.95~103 (1992)
  70. J. M. Rassias, "On the stability of the non-linear Euler-Lagrange functional equation in real normed linear spaces", J. Math. Phys. Sci, 28(5), pp.231~235 (1994)
  71. J. M. Rassias, "On the stability of a multi-dimensional Cauchy type functional equation, Ge- ometry, analysis and mechanics", pp.365~376 (1994), World Sci. Publ.
  72. J. M. Rassias, "On the stability of the linear mapping in Banach spaces", Proc. Amer. Math. Soc, 72(2), pp.297~300 (1978)
  73. J. M. Rassias, "New characterization of inner product spaces", Bull. Sci. Math, 108(1), pp.95~99 (1984)
  74. Th. M. Rassias, "On the behaviour of mappings which do not satisfy Hyers- Ulam stability", Proc. Amer. Math. Soc, 114, pp.989~993 (1992)
  75. K. Ravi, "Ulam stability for the orthogonally general Euler-Lagrange type functional equation", Int. J. Math. Stat, 3, pp.36~46 (2008)
  76. B. Schweizer, "Probabilistic Metric Spaces" (1983), Elsevier North Holand
  77. A. N. Serstnev, "On the motion of a random normed space", Dokl. Akad. Nauk SSSR, 149, pp.280~283 (1963)
  78. S. Shakeri, "Stability of the quadratic functional equation in non-Archimedean L-fuzzy normed spaces", Int. J. Nonlinear Anal. Appl, 1(2), pp.72~83 (2010)
  79. F. Skof, "Local properties and approximation of operators, Geometry of Banach spaces and related topics (Italian) (Milan, 1983)", Rend. Sem. Mat. Fis. Milano, 53, pp.113~129 (1983)
  80. S. M. Ulam, "Problems in Modern Mathematics, Chapter VI, Science Editions" (1964), Wiley

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