본문 바로가기
KERD
논문KCI 등재

The stability of the sine and cosine functional equations in Schwartz distributions

2

조회

0

다운로드

3

인용

0

참고문헌

키워드

주제분류수학

초록

We prove the Hyers-Ulam stability of the sine and cosine functional equations in the spaces of generalized functions such as Schwartz distributions, Fourier hyperfunctions, and Gelfand generalized functions.

Abstract

We prove the Hyers-Ulam stability of the sine and cosine functional equations in the spaces of generalized functions such as Schwartz distributions, Fourier hyperfunctions, and Gelfand generalized functions.

참고문헌 (21)

  1. J. Aczel, "Lectures on Functional Equations and Their Applications, Mathematics in Science and Engineering" (1966), Academic Press
  2. J. Aczel, "Equations in Several Variables, Encyclopedia of Mathematics and its Applications", pp.31~ (1989), Cambridge University Press
  3. J. A. Baker, "On a functional equation of Acz´el and Chung", Aequationes Math., 46(1), pp.99~111 (1993)
  4. J. A. Baker, "The stability of the cosine equation", Proc. Amer. Math. Soc., 80(3), pp.411~416 (1980)
  5. J. A. Baker, "Functional equations, tempered distributions and Fourier transforms", Trans. Amer. Math. Soc., 315(1), pp.57~68 (1989)
  6. J. A. Baker, "Distributional methods for functional equations", Aequationes Math., 62(1), pp.136~142 (2001)
  7. J.-Y. Chung, "A distributional version of functional equations and their stabilities", Nonlinear Anal., 62(6), pp.1037~1051 (2005)
  8. 1968, , pp.2, ~
  9. L. Hormander, , pp.256~ (1983), Springer-Verlag
  10. D. H. Hyers, "On the stability of the linear functional equation", Proc. Nat. Acad. Sci. U.S. A., 27, pp.222~224 (1941)
  11. D. H. Hyers, "Stability of Functional Equations in Several Variables" (1998), Birkhauser Boston, Inc
  12. D. H. Hyers, "Approximate homomorphisms", Aequationes Math., 44(2), pp.125~153 (1992)
  13. S.-M. Jung, "Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis" (2001), Hadronic Press, Inc
  14. Th. M. Rassias, "On the stability of functional equations in Banach spaces", J. Math. Anal. Appl., 251(1), pp.264~284 (2000)
  15. Th. M. Rassias, "On the stability of the linear mapping in Banach spaces", Proc. Amer. Math. Soc., 72(2), pp.297~300 (1978)
  16. L. Schwartz, "Th´eorie des distributions" (1966), Hermann
  17. L. Szekelyhidi, "The stability of the sine and cosine functional equations", Proc. Amer. Math. Soc., 110(1), pp.109~115 (1990)
  18. L. Szekelyhidi, "The stability of d’Alembert type functional equations", Acta Sci. Math. (Szeged), 44(3), pp.313~320 (1982)
  19. I. Tyrala, "The stability of d’Alembert’s functional equation", Aequationes Math., 69(3), pp.250~256 (2005)
  20. S. M. Ulam, "A Collection of Mathematical Problems" (1960), Interscience Publishers
  21. D. V. Widder, "The Heat Equation" (1975), Academic Press

이 간행물의 다른 논문 (18건)