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Khodaei, H., Rassias, Th. M.. (1388). Approximately generalized additive functions in several variables. هنرهای کاربردی, 1(1), 22-41. doi: 10.22075/ijnaa.2010.66
H. Khodaei; Th. M. Rassias. "Approximately generalized additive functions in several variables". هنرهای کاربردی, 1, 1, 1388, 22-41. doi: 10.22075/ijnaa.2010.66
Khodaei, H., Rassias, Th. M.. (1388). 'Approximately generalized additive functions in several variables', هنرهای کاربردی, 1(1), pp. 22-41. doi: 10.22075/ijnaa.2010.66
Khodaei, H., Rassias, Th. M.. Approximately generalized additive functions in several variables. هنرهای کاربردی, 1388; 1(1): 22-41. doi: 10.22075/ijnaa.2010.66

Approximately generalized additive functions in several variables

International Journal of Nonlinear Analysis and Applications
مقاله 4، دوره 1، شماره 1، فروردین 2010، صفحه 22-41    اصل مقاله (282.59 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2010.66
نویسندگان
H. Khodaei* 1؛ Th. M. Rassias2
1Department of Mathematics, Semnan University P. O. Box 35195-363, Semnan, Iran.
2Department of Mathematics, National Technical University of Athens, Zografou, Campus 15780 Athens, Greece
تاریخ دریافت: 19 خرداد 1388،  تاریخ بازنگری: 12 آذر 1388،  تاریخ پذیرش: 27 آذر 1388 
چکیده
The goal of this paper is to investigate the solution and stability in random normed spaces, in non--Archimedean spaces and also in $p$--Banach spaces and finally the stability using the alternative fixed point of generalized additive functions in several variables.
کلیدواژه‌ها
Additive function؛ $p$--Banach spaces؛ Random normed spaces؛ Non-–Archimedean spaces؛ Fixed point method؛ Generalized Hyers–-Ulam stability
مراجع
  1. J. Aczel and J. Dhombres, Functional Equations in Several Variables, Cambridge University Press, 1989.
  2. R.P. Agarwal, B. Xu and W. Zhang, Stability of functional equations in single variable, J. Math. Anal. Appl. 228 (2003) 852–869.
  3. C. Alsina, On the stability of a functional equation arising in probabilistic normed spaces, General Inequalities. 5 (1987) 263-271.
  4. D. Amir, Characterizations of Inner Product Spaces, Birkhuser, Basel, 1986.
  5. T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan. 2 (1950) 64–66.
  6. L.M. Arriola and W.A. Beyer, Stability of the Cauchy functional equation over p-adic fields, Real Analysis Exchange. 31 (2005/2006) 125-132.
  7. J.A. Baker, The stability of certain functional equations, Proc. Amer. Math. Soc. 112 (1991) 729–732.
  8. E. Baktash, Y.J. Cho, M. Jalili, R. Saadati and S.M. Vaezpour, On the stability of cubic mappings and quadratic mappings in random normed spaces, J. Inequal. Appl., Volume 2008, Article ID 902187.
  9. Y. Benyamini and J. Lindenstrauss, Geometric Nonlinear Functional Analysis, vol. 1, Colloq. Publ. vol. 48, Amer. Math. Soc., Providence, RI, 2000.
  10. S.S. Chang, Y.J. Cho and S.M. Kang, Nonlinear Operator Theory in Probabilistic Metric Spaces, Nova Science Publishers, Inc., New York, 2001.
  11. L. C˘adariu and V. Radu, On the stability of the Cauchy functional equation: a fixed point approach, Grazer Mathematische Berichte, 346 (2004) 43-52.
  12. L. C˘adariu and V. Radu, Fixed points and the stability of Jensens functional equation, Journal of Inequalities in Pure and Applied Mathematics, vol. 4, no. 1, article 4, 7 pages, 2003.
  13. P.W. Cholewa, Remarks on the stability of functional equations, Aequationes Math. 27 (1984) 76–86.
  14. P. Czerwik, Functional Equations and Inequalities in Several Variables, World Scientific Publishing Company, New Jersey, Hong Kong, Singapore, London, 2002.
  15. S. Czerwik, On the stability of the quadratic mapping in normed spaces, Abh. Math. Sem. Univ. Hamburg. 62 (1992) 59–64.
  16. M. Eshaghi Gordji and H. Khodaei, Solution and stability of generalized mixed type cubic, quadratic and additive functional equation in quasi–Banach spaces, Nonlinear Analysis.-TMA. 71 (2009) 5629–5643.
  17. M. Eshaghi Gordji and H. Khodaei, On the Generalized Hyers-Ulam-Rassias Stability of Quadratic Functional Equations, Abstract and Applied Analysis Volume 2009, Article ID 923476, 11 pages.
  18. M. Eshaghi Gordji, H. Khodaei and C. Park, A fixed point approach to the Cauchy-Rassias stability of general Jensen type quadratic-quadratic mappings, (To appear).
  19. V.A. Faizev, Th.M. Rassias and P.K. Sahoo, The space of (ψ, γ)–additive mappings on semigroups, Trans. Amer. Math. Soc. 354 (11) (2002) 4455–4472.
  20. Z. Gajda, On stability of additive mappings, Int. J. Math. Math. Sci. 14 (1991) 431–434.
  21. P. Gˇavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994) 431-436.
  22. P. Gˇavruta, An answer to a question of Th.M. Rassias and J. Tabor on mixed stability of mappings, Bul. Stiint. Univ. Politeh. Timis. Ser. Mat. Fiz. 42 (56) (1997) 1–6.
  23. P. Gˇavruta, On the Hyers–Ulam–Rassias stability of mappings, Recent Progress in Inequalities. 430 (1998) 465–469.
  24. P. Gˇavruta, An answer to a question of John M. Rassias concerning the stability of Cauchy equation, in: Advances in Equations and Inequalities, Hadronic Math. Ser. (1999) 67–71.
  25. P. Gˇavruta, On a problem of G. Isac and Th.M. Rassias concerning the stability of mappings, J. Math. Anal. Appl. 261 (2001) 543–553.
  26. P. Gˇavruta, On the Hyers–Ulam–Rassias stability of the quadratic mappings, Nonlinear Funct. Anal. Appl. 9 (2004) 415–428.
  27. P. Gˇavruta, M. Hossu, D. Popescu and C. Cˇaprˇau, On the stability of mappings and an answer to a problem of Th.M. Rassias, Ann. Math. Blaise Pascal. 2 (1995) 55–60.
  28. A. Grabiec, The generalized Hyers–Ulam stability of a class of functional equations, Publ. Math. Debrecen. 48 (1996) 217–235.
  29. O. Hadˇzi´c and E. Pap, Fixed Point Theory in PM Spaces, Kluwer Academic Publishers, Dordrecht. 2001.
  30. O. Hadˇzi´c, E. Pap and M. Budincevi´c, Countable extension of triangular norms and their applications to the fixed point theory in probabilistic metric spaces, Kybernetica, 38 (3) (2002) 363–381.
  31. K. Hensel, Uber eine neue Begrundung der Theorie der algebraischen Zahlen, Jahresber. Deutsch. Math. Verein. 6 (1897) 83-88.
  32. D.H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. 27 (1941) 222–224.
  33. D.H. Hyers, G. Isac and Th.M. Rassias, Stability of Functional Equations in Several Variables, Birkhuser, Basel, 1998.
  34. D.H. Hyers and Th.M. Rassias, Approximate homomorphisms, Aequationes Math. 44 (1992) 125–153.
  35. D.H. Hyers, G. Isac and Th.M. Rassias, Topics in Nonlinear Analysis and Applications, World Scientific Publishing Company, 1997.
  36. G. Isac and Th.M. Rassias, Stability of ψ–additive mappings: Applications to nonlinear analysis, Internat. J. Math. Math. Sci. 19 (1996) 219–228.
  37. P. Jordan and J. Neumann, On inner products in linear metric spaces, Ann. Math. 36 (1935) 719–723.
  38. S.-M. Jung, Hyers–Ulam–Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press Inc., Palm Harbor, Florida, 2001.
  39. S.-M. Jung and T.-S. Kim, A fixed point approach to stability of cubic functional equation, Bol. Soc. Mat. Mexicana 12 (2006) 51–57.
  40. Y.S. Jung and L.S. Chang, The stability of a cubic type functional equation with The fixed point alternative, J. Math. Anal. Appl. 306 (2005) 752–760.
  41. Pl. Kannappan, Quadratic functional equation and inner product spaces, Results Math. 27 (1995) 368–372.
  42. A. Khrennikov, Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models, Kluwer Academic Publishers, Dordrecht, 1997.
  43. B. Margolis and J.B. Diaz, A fixed point theorem of the alternative for contractions on the generalized complete metric space, Bull. Amer. Math. Soc. 126 74 (1968) 305–309.
  44. D. Mihet¸, Fuzzy stability of additive mappings in non-Archimedean fuzzy normed spaces, Fuzzy Sets and Systems (communicated).
  45. D. Mihet¸, The probabilistic stability for a functional equation in a single variable, Acta Math. Hungar. 123 (2009) 249–256.
  46. D. Mihet¸, The fixed point method for fuzzy stability of the Jensen functional equation, Fuzzy Sets and Systems. 160 (2009) 1663–1667.
  47. D. Mihet¸ and V. Radu, On the stability of the additive Cauchy functional equation in random normed spaces, J. Math. Anal. Appl. 343 (2008) 567–572.
  48. D. Mihet¸, R. Saadati and S.M. Vaezpour, The stability of the quartic functional equation in random normed spaces, Acta Appl. Math., DOI: 10.1007/s10440-009-9476-7.
  49. D. Mihet¸, R. Saadati and S.M. Vaezpour, The stability of an additive functional equation in Menger probabilistic ϕ-normed spaces, Math. Slovak, in press.
  50. A.K. Mirmostafaee, M. Mirzavaziri and M.S. Moslehian, Fuzzy stability of the Jensen functional equation, Fuzzy Sets and Systems. 159 (2008) 730–738.
  51. A.K. Mirmostafaee and M.S. Moslehian, Fuzzy versions of Hyers-Ulam-Rassias theorem, Fuzzy Sets and Systems. 159 (2008) 720–729.
  52. A.K. Mirmostafaee and M.S. Moslehian, Fuzzy approximately cubic mappings, Inform. Sci. 178 (2008) 3791–3798.
  53. M. Mirzavaziri and M.S. Moslehian, A fixed point approach to stability of a quadratic equation, Bull. Braz. Math. Soc. 37 (2006) 361–376.
  54. M.S. Moslehian and T.M. Rassias, Stability of functional equations in non-Archimedean space, Applicable Analysis and Discrete Mathematics. 1 (2007) 325-334.
  55. V. Radu, The fixed point alternative and the stability of functional equations, Fixed Point Theory. 4 (2003) 91-96.
  56. Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978) 297–300.
  57. Th.M. Rassias, New characterization of inner product spaces, Bull. Sci. Math. 108 (1984) 95–99.
  58. Th.M. Rassias, Functional Equations, Inequalities and Applications, Kluwer Academic Publishers Co., Dordrecht, Boston, London, 2003.
  59. Th.M. Rassias, Problem 16; 2, Report of the 27th International Symp. on Functional Equations, Aequationes Math. 39 (1990) 292–293.
  60. Th.M. Rassias, On the stability of the quadratic functional equation and its applications, Studia Univ. Babes-Bolyai. XLIII (1998) 89–124.
  61. Th.M. Rassias, The problem of S.M. Ulam for approximately multiplicative mappings, J. Math. Anal. Appl. 246 (2000) 352–378.
  62. Th.M. Rassias, On the stability of functional equations in Banach spaces, J. Math. Anal. Appl. 251 (2000) 264–284.
  63. Th.M. Rassias, On the stability of functional equations and a problem of Ulam, Acta Appl. Math. 62 (2000) 23–130.
  64. Th.M. Rassias and P. Semrl, ˇ On the behaviour of mappings which do not satisfy Hyers-Ulam stability, Proc. Amer. Math. Soc. 114 (1992) 989–993.
  65. Th.M. Rassias and P. Semrl, ˇ On the Hyers-Ulam stability of linear mappings, J. Math. Anal. Appl. 173 (1993) 325–338.
  66. Th.M. Rassias and K. Shibata, Variational problem of some quadratic functionals in complex analysis, J. Math. Anal. Appl. 228 (1998) 234–253.
  67. A. M. Robert, A Course in p-adic Analysis, Springer-Verlag, New York, 2000.
  68. S. Rolewicz, Metric Linear Spaces, PWN-Polish Sci. Publ./Reidel, Warszawa/Dordrecht, 1984.
  69. I.A. Rus, Principles and Applications of Fixed Point Theory, Ed. Dacia, Cluj-Napoca, 1979 (in Romanian).
  70. R. Saadati, S.M. Vaezpour and Y.J. Cho, A note on the ”On the stability of cubic mappings and quadratic mappings in random normed spaces”, J. Inequal. Appl., Volume 2009, Article ID 214530, 6 pages.
  71. B. Schweizer and A. Sklar, Probabilistic Metric Spaces, Elsevier, North Holand, New York, 1983.
  72. A.N. Serstnev, ˇ On the notion of a random normed space, Dokl. Akad. Nauk SSSR 149 (1963) 280-283 (in Russian).
  73. J. Tabor, stability of the Cauchy functional equation in quasi-Banach spaces, Ann. Polon. Math. 83 (2004) 243–255.
  74. S.M. Ulam, Problems in Modern Mathematics, Chapter VI, science Editions., Wiley, New York, 1964.
  75. A.C.M. Van rooij, Non-Archimedean functional analysis, in: Monographs and Textbooks in Pure and Applied Math, vol. 51, Marcel Dekker, New York, 1978.
  76. V.S. Vladimirov, I.V. Volovich and E.I. Zelenov, p–adic Analysis and Mathematical Physics, World Scientific, 1994.
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