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Approximate homomorphisms and derivation in multi-Banach algebras

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Using fixed point methods, we prove the generalized Hyers-Ulam stability of homomorphisms in multi-Banach algebras and derivations on multi-Banach algebras for the additive functional equation... [formula]
Rocznik
Strony
23--38
Opis fizyczny
Bibliogr. 34 poz.
Twórcy
autor
autor
autor
autor
  • Department of Mathematics Education and RINS, Gyeongsang National University Chinju 660-701, Korea, yjcho@gnu.ac.kr
Bibliografia
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  • [3] L. Cǎdariu and V. Radu, Fixed points and the stability of Jensen's functional equation, J. Inequal. Pure Appl. Math. 4, Article 4 (2003).
  • [4] L. Cǎdariu and V. Radu, On the stability of the Cauchy functional equation: a fixed point approach, Grazer Math. Ber. 346 (2004), 43-52.
  • [5] H.G. Dales and M.E. Polyakov, Multi-normed spaces and multi-Banach algebras (preprint).
  • [6] H.G. Dales and M.S. Moslehian, Stability of mappings on multi-normed spaces, Glasg. Math. J. 49 (2007), 321-332.
  • [7] H.G. Dales, Banach Algebras and Automatic Continuity, London Math. Soc. Monographs, New Series 24, Oxford University Press, Oxford, 2000.
  • [8] J. Diaz and B. Margolis, A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Amer. Math. Soc. 74 (1968), 305-309.
  • [9] P. Gǎvruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), 431-436.
  • [10] D.H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. USA 27 (1941), 222-224.
  • [11] M.S. Moslehian, On the orthogonal stability of the Pexiderized quadratic equation, J. Differ. Equat. Appl. 11 (2005), 999-1004.
  • [12] M.S. Moslehian, K. Nikodem and D. Popa, Asymptotic aspect of the quadratic functional equation in multi-normed spaces, J. Math. Anal. Appl. 355 (2009), 717-724.
  • [13] M.S. Moslehian, Superstability of higher derivations in Multi-Banach algebras, Tamsui Oxford J. Math. Sci. 24 (2008), 417-427.
  • [14] C. Park, On the stability of the linear mapping in Banach modules, J. Math. Anal. Appl. 275 (2002), 711-720.
  • [15] C. Park, Modified Trif 's functional equations in Banach modules over a C*-algebra and approximate algebra homomorphisms, J. Math. Anal. Appl. 278 (2003), 93-108.
  • [16] C. Park, On an approximate automorphism on a C*-algebra, Proc. Amer. Math. Soc. 132 (2004), 1739-1745.
  • [17] C. Park, Lie -homomorphisms between Lie C*-algebras and Lie -derivations on Lie C*-algebras, J. Math. Anal. Appl. 293 (2004), 419-434.
  • [18] C. Park, Homomorphisms between Lie J C*-algebras and Cauchy-Rassias stability of Lie JC*-algebra derivations, J. Lie Theory 15 (2005), 393-414.
  • [19] C. Park, Homomorphisms between Poisson JC*-algebras, Bull. Braz. Math. Soc. 36 (2005), 79-97.
  • [20] C. Park, Hyers-Ulam-Rassias stability of a generalized Euler-Lagrange type additive mapping and isomorphisms between C_-algebras, Bull. Belgian Math. Soc. Simon Stevin 13 (2006), 619-631.
  • [21] C. Park, Fixed points and Hyers-Ulam-Rassias stability of Cauchy-Jensen functional equations in Banach algebras, Fixed Point Theory and Appl. 2007, Article ID 50175 (2007).
  • [22] C. Park and J. Cui, Generalized stability of C*-ternary quadratic mappings, Abstr. Appl. Anal. 2007, Article ID 23282 (2007).
  • [23] C. Park and J. Hou, Homomorphisms between C*-algebras associated with the Trif functional equation and linear derivations on C*-algebras, J. Korean Math. Soc. 41 (2004), 461-477.
  • [24] C. Park and A. Najati, Homomorphisms and derivations in C*-algebras, Abstr. Appl. Anal. 2007, Article ID 80630 (2007).
  • [25] C. Park and J. Park, Generalized Hyers-Ulam stability of an Euler-Lagrange type additive mapping, J. Differ. Equat. Appl. 12 (2006), 1277-1288.
  • [26] V. Radu, The fixed point alternative and the stability of functional equations, Fixed Point Theory 4 (2003), 91-96.
  • [27] Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.
  • [28] Th.M. Rassias, Problem 16; 2, Report of the 27th Internat. Symp. on Functional Equations, Aequat. Math. 39 (1990), 292-293; 309.
  • [29] Th.M. Rassias, The problem of S.M. Ulam for approximately multiplicative mappings, J. Math. Anal. Appl. 246 (2000), 352-378.
  • [30] Th.M. Rassias, On the stability of functional equations in Banach spaces, J. Math. Anal. Appl. 251 (2000), 264-284.
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  • [34] S.M. Ulam, A Collection of the Mathematical Problems, Interscience Publ. New York, 1960.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS8-0012-0011
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