대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제43권4호
  • /
  • Pages.737-745
  • /
  • 2006
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

ON THE STABILITY OF INVOLUTIVE A-QUADRATIC MAPPINGS

  • Park, Won-Gil (NATIONAL INSTITUTE FOR MATHEMATICAL SCIENCES) ;
  • Bae, Jae-Hyeong (DEPARTMENT OF MATHEMATICS AND APPLIED MATHEMATICS, KYUNGHEE UNIVERSITY)
  • 발행 : 2006.11.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we will investigate the Hyers-Ulam stability of an involutive A-quadratic mapping.

키워드

참고문헌

  1. J. Aczel and J. Dhombres, Functional equations in several variables, Cambridge Univ. Press, Cambridge, 1989
  2. J.-H. Bae and K.-W. Jun, On the generalized Hyers-Ulam-Rassias stability of an n-dimensional quadratic functional equation, J. Math. Anal. Appl. 258 (2001), no. 1, 183-193 https://doi.org/10.1006/jmaa.2000.7372
  3. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer-Verlag New York, Heidelberg and Berlin, 1973
  4. S. Czerwik, On the stability of the quadratic mapping in normed spaces, Abh. Math. Sem. Univ. Hamburg. 62 (1992), 59-64 https://doi.org/10.1007/BF02941618
  5. P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approxi-mately additive mappings, J. Math. Anal. Appl. 184 (1994), no. 3, 431-436 https://doi.org/10.1006/jmaa.1994.1211
  6. D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A. 27 (1941), 222-224
  7. K.-W. Jun, J.-H. Bae, and Y.-H. Lee, On the Hyers-Ulam-Rassias stability of ann-dimensional Pexiderized quadratic equation, Math. Ineq. Appl. 7 (2004), no. 1, 63-77
  8. K.-W. Jun, J.-H. Bae, and W.-G. Park, Partitioned functional inequalities in Banach modules and approximate algebra homomorphisms, Math. Ineq. Appl. 6 (2003), no. 4, 715-726
  9. D. H. Hyers, G. Isac, and Th. M. Rassias, Stability of Functional Equations in Several Variables, Birkhauser, Basel-Boston, 1998
  10. R. Kadison and G. Pedersen, Means and convex combinations of unitary operators, Math. Scand. 57 (1985), no. 2, 249-266 https://doi.org/10.7146/math.scand.a-12116
  11. C.-G. Park, Functional equations in Banach modules, Indian J. Pure Appl. Math. 33 (2002), no. 7, 1077-1086
  12. C.-G. Park, Multilinear mappings in Banach modules over a $C^{*}$-algebra, Indian J. Pure Appl. Math., to appear
  13. C.-G. Park and J.-K. Shin, Generalized Jensens equations in Banach modules, Indian J. Pure Appl. Math. 33 (2002), no. 12, 1867-1875
  14. Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), no. 2, 297-300
  15. F. Skof, Local properties and approximation of operators, Rend. Sem. Mat. Fis. Milano 53 (1983), 113-129 https://doi.org/10.1007/BF02924890
  16. S. M. Ulam, Problems in Modern Mathematics, Wiley, New York, 1964
  17. J. Vukman, Some functional equations in Banach algebras and an application, Proc. Amer. Math. Soc. 100 (1987), no. 1, 133-136