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Stability of n-dimensional additive functional equation in generalized 2-normed space

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Języki publikacji
EN
Abstrakty
EN
In this paper, the author established the general solution and generalized Ulam–Hyers–Rassias stability ofn-dimensional additive functional equation (…) in generalized 2-normed space.
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Rocznik
Strony
319--330
Opis fizyczny
Bibliogr. 32 poz.
Twórcy
autor
  • Department of Mathematics Government Arts College Tiruvannamalai - 606 603 Tamilnadu, India
Bibliografia
  • [1] J. Aczel, J. Dhombres, Functional Equations in Several Variables, Cambridge Univ. Press, 1989.
  • [2] T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math.Soc. Japan 2 (1950), 64–66.
  • [3] M. Arunkumar, Stability of a cubic functional equation in dq-normed space, Int. J. Pure Appl. Math. 57 (2009), 241–250.
  • [4] M. Arunkumar, Three dimensional quartic functional equation in fuzzy normed spaces, Far East J. Appl. Math. 41(2) (2010), 88–94.
  • [5] M. Arunkumar, Solution and stability of Arun-additive functional equations, Int. J. Math. Sci. Eng. Appl. 4(3) August 2010, 33–46.
  • [6] M. Arunkumar, S. Murthy, G. Ganapathy, S. Karthikeyan, Stability of the generalized Arun-additive functional equation in intutionistic fuzzy normed spaces, Int. J. Math. Sci. Eng. Appl. 4(5) December 2010, 135–146.
  • [7] M. Arunkumar, S. Jayanthi, Solution and stability of additive and quadratic functional equation in generalized 2-normed spaces, Int. J. Pure Appl. Math., accepted.
  • [8] M. Arunkumar, Solution and stability of a functional equation originating from arithmetic mean of consecutive Terms of an arithmetic progression, Functiomal Equations in Mathematical Analysis, Dedicated to the Memory of the 100th Anniversary of S. M. Ulam, SPRINGER, accepted.
  • [9] M. Arunkumar, G. Ganapathy, S. Murthy, Stability of a functional equation having nth order solution in generalized 2-normed spaces, Int. J. Math. Sci. Eng. Appl. 5(4) July 2011, 361–369.
  • [10] D. G. Bourgin, Classes of transformations and bordering transformations, Bull. Amer. Math. Soc. 57 (1951), 223–237.
  • [11] S. Czerwik, Functional Equations and Inequalities in Several Variables, World Scientific, River Edge, NJ, 2002.
  • [12] D. O. Lee, Hyers–Ulam stability of an addtiive type functional equation, J. Appl. Math. Comput. 13(1–2) (2003), 471–477.
  • [13] I. Fenyö, Osservazioni su alcuni teoremi di D. H. Hyers, Istit. Lombardo Accad. Sci. Lett. Rend. A 114 (1980), 235–242.
  • [14] I. Fenyö, On an inequality of P. W. Cholewa, in General Inequalities 5, Internat. Schrifenreiche Number. Math., Vol. 80, Birkhauser, Basel, MA, 1987, 277–280.
  • [15] Z. Gajda, R. Ger, Subadditive multifunctions and Hyers–Ulam stability, in General Inequalites 5, Internat. Schrifenreiche Number. Math., Vol. 80, Birkhauser, Basel, 1987.
  • [16] P. Gavruta, A generalization of the Hyers–Ulam–Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), 431–436.
  • [17] H. Haruki, Th. M. Rassias, New characterizations of some mean values, J. Math. Anal. Appl. 202 (1996), 333–348.
  • [18] D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222–224.
  • [19] D. H. Hyers, G. Isac, Th. M. Rassias, Stability of Functional equations in Several Variables, Birkhauser, Basel, 1998.
  • [20] S. M. Jung, Hyers–Ulam–Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press, Palm Harbor, 2001.
  • [21] Pl. Kannappan, Quadratic functional equation inner product spaces, Results Math. 27(3–4) (1995), 368–372.
  • [22] M. Moslehian, Th. M. Rassias, Stability of functional equations in non-Archimedian spaces, Appl. Anal. Discrete Math. 1(2) (2007), 325–334.
  • [23] J. M. Rassias, On approximation of approximately linear mappings by linear mappings, J. Funct. Anal. 46 (1982), 126–130.
  • [24] J. M. Rassias, On approximation of approximately linear mappings by linear mappings, Bull. Sci. Math. 108 (1984), 445–446.
  • [25] Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297–300.
  • [26] Th. M. Rassias, P. Semrl, On the behavior of mappings which do not satisfy Hyers–Ulam stability, Proc. Amer. Math. Soc. 114 (1992), 989–993.
  • [27] Th. M. Rassias, On the stability of functional equations and a problem of Ulam, Acta. Appl. Math. 62 (2000), 23–130.
  • [28] Th. M. Rassias, Functional Equations, Inequalities and Applications, Kluwer Acedamic Publishers, Dordrecht, Boston, London, 2003.
  • [29] K. Ravi, M. Arunkumar, On an n dimensional additive functional equation with fixed point alternative, Proceedings of ICMS 2007, Malaysia.
  • [30] K. Ravi, M. Arunkumar, J. M. Rassias, On the Ulam stability for the orthogonally general Euler–Lagrange type functional equation, Internat. J. Math. Sci., Autumn 3(8) (2008), 36–47.
  • [31] K. Ravi, M. Arunkumar, P. Narasimman, Fuzzy stability of an additive functional equation, Internat. J. Math. Sci., Autumn 9(A11) (2011), 88–105.
  • [32] S. M. Ulam, Problems in Modern Mathematics, Science Editions, Wiley, New York, 1964.
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Typ dokumentu
Bibliografia
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