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ORTHOGONALITY AND LINEAR MAPPINGS IN BANACH MODULES

윤성식
한국수학교육학회|2015.11|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제22권 제4호|pp. 343-357

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참고문헌

키워드

fixed pointHyers-Ulam stabilityorthogonality spacenon-Archimedean Banach module over C*-algebra
주제분류수학

초록

Using the fixed point method, we prove the Hyers-Ulam stability of linear mappings in Banach modules over a unital C*-algebra and in non-Archimedean Banach modules over a unital C*-algebra associated with the orthogonally Cauchy- Jensen additive functional equation.

Abstract

Using the fixed point method, we prove the Hyers-Ulam stability of linear mappings in Banach modules over a unital C*-algebra and in non-Archimedean Banach modules over a unital C*-algebra associated with the orthogonally Cauchy- Jensen additive functional equation.

참고문헌 (45)

  1. J. Alonso, "Orthogonality in normed linear spaces: a survey I. Main properties", Extracta Math, 3, pp.1~15 (1988)
  2. J. Alonso, "Orthogonality in normed linear spaces: a survey II. Relations between main orthogonalities", Extracta Math, 4, pp.121~131 (1989)
  3. G. Birkhoff, "Orthogonality in linear metric spaces", Duke Math. J, 1, pp.169~172 (1935)
  4. L. Cadariu, "Fixed points and the stability of Jensen's functional equation", J. Inequal. Pure Appl. Math, 4(1) (2003)
  5. L. Cadariu, "On the stability of the Cauchy functional equation: a fixed point approach", Grazer Math. Ber, 346, pp.43~52 (2004)
  6. L. Cadariu, "Fixed point methods for the generalized stability of functional equations in a single variable", Fixed Point Theory and Applications, 2008 (2008)
  7. S.O. Carlsson, "Orthogonality in normed linear spaces", Ark. Mat, 4, pp.297~318 (1962)
  8. P.W. Cholewa, "Remarks on the stability of functional equations", Aequationes Math, 27, pp.76~86 (1984)
  9. S. Czerwik, "On the stability of the quadratic mapping in normed spaces", Abh. Math. Sem. Univ. Hamburg, 62, pp.59~64 (1992)
  10. S. Czerwik, "Functional Equations and Inequalities in Several Variables" (2002), World Scientific Publishing Company
  11. S. Czerwik, "Stability of Functional Equations of Ulam-Hyers-Rassias Type" (2003), Hadronic Press
  12. D. Deses, "On the representation of non-Archimedean objects", Topology Appl, 153, pp.774~785 (2005)
  13. J. Diaz, "A fixed point theorem of the alternative for contractions on a generalized complete metric space", Bull. Amer. Math. Soc., 74, pp.305~309 (1968)
  14. C.R. Diminnie, "A new orthogonality relation for normed linear spaces", Math. Nachr, 114, pp.197~203 (1983)
  15. F. Drljevic, "On a functional which is quadratic on A-orthogonal vectors", Publ. Inst. Math.(Beograd), 54, pp.63~71 (1986)
  16. M. Fochi, "Functional equations in A-orthogonal vectors", Aequationes Math, 38, pp.28~40 (1989)
  17. R. Ger, "Stability of the orthogonal additivity", Bull. Polish Acad. Sci. Math, 43, pp.143~151 (1995)
  18. S. Gudder, "Orthogonally additive and orthogonally increasing func-tions on vector spaces", Pacific J. Math, 58, pp.427~436 (1975)
  19. K. Hensel, "Ubereine news Begrundung der Theorie der algebraischen Zahlen", Jahresber. Deutsch. Math. Verein, 6, pp.83~88 (1897)
  20. D.H. Hyers, "On the stability of the linear functional equation", Proc. Nat. Acad. Sci. U.S.A, 27, pp.222~224 (1941)
  21. D.H. Hyers, "Stability of Functional Equations in Several Variables" (1998), BirkhÄauser
  22. G. Isac, "Stability of Ã-additive mappings: Appications to nonlinear analysis", Internat. J. Math. Math. Sci., 19, pp.219~228 (1996)
  23. R.C. James, "Orthogonality in normed linear spaces", Duke Math. J, 12, pp.291~302 (1945)
  24. R.C. Jame, "Orthogonality and linear functionals in normed linear spaces", Trans. Amer. Math. Soc, 61, pp.265~292 (1947)
  25. S. Jung, "Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis" (2001), Hadronic Press
  26. R.V. Kadison, "Fundamentals of the Theory of Operator Algebras" (1983), Academic Press
  27. A.K. Katsaras, "Tensor products of non-Archimedean weighted spaces of continuous functions", Georgian Math. J, 6, pp.33~44 (1999)
  28. A. Khrennikov, "Non-Archimedean analysis: quantum paradoxes, dynamical systems and biological models" (1997), Kluwer Academic Publishers
  29. D. Mihet, "On the stability of the additive Cauchy functional equation in random normed spaces", J. Math. Anal. Appl, 343, pp.567~572 (2008)
  30. M. Mirzavaziri, "A fixed point approach to stability of a quadratic equation", Bull. Braz. Math. Soc, 37, pp.361~376 (2006)
  31. M.S. Moslehian, "On the orthogonal stability of the Pexiderized quadratic equation", J. Difference Equat. Appl, 11, pp.999~1004 (2005)
  32. M.S. Moslehian, "On the stability of the orthogonal Pexiderized Cauchy equation", J. Math. Anal. Appl, 318, pp.211~223 (2006)
  33. M.S. Moslehian, "Orthogonal stability of additive type equations", Aequationes Math, 73, pp.249~259 (2007)
  34. M.S. Moslehian, "A Mazur-Ulam theorem in non-Archimedean normed spaces", Nonlinear Anal.TMA, 69, pp.3405~3408 (2008)
  35. P.J. Nyikos, "On some non-Archimedean spaces of Alexandrof and Urysohn", Topology Appl, 91, pp.1~23 (1999)
  36. L. Paganoni, "Conditional function equations and orthogonal additivity", Aequationes Math, 50, pp.135~142 (1995)
  37. C. Park, "Fixed points and Hyers-Ulam-Rassias stability of Cauchy-Jensen functional equations in Banach algebras", Fixed Point Theory and Applications, 2007 (2007)
  38. C. Park, "Generalized Hyers-Ulam-Rassias stability of quadratic functional equations:a fixed point approach", Fixed Point Theory and Applications, 2008 (2008)
  39. C. Park, "Generalized Hyers-Ulam stability of an Euler-Lagrange type addi-tive mapping", J. Difference Equat. Appl, 12, pp.1277~1288 (2006)
  40. A.G. Pinsker, "Sur une fonctionnelle dans l'espace de Hilbert. C. R. (Dokl.)", Acad. Sci. URSS, n. Ser., 20, pp.411~414 (1938)
  41. V. Radu, "The fixed point alternative and the stability of functional equations", Fixed Point Theory, 4, pp.91~96 (2003)
  42. Th.M. Rassias, "On the stability of the linear mapping in Banach spaces", Proc. Amer. Math. Soc, 72, pp.297~300 (1978)
  43. Th.M. Rassias, "On the stability of the quadratic functional equation and its applications, Studia Univ", Babes-Bolyai Math, 43, pp.89~124 (1998)
  44. Th.M. Rassias, "The problem of S.M. Ulam for approximately multiplicative mappings", J. Math. Anal. Appl, 246, pp.352~378 (2000)
  45. Th.M. Rassias, "On the stability of functional equations in Banach spaces", J. Math. Anal. Appl, 251, pp.264~284 (2000)

관련 논문AI추천

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