DOI QR코드

DOI QR Code

HYERS-ULAM STABILITY OF TRIGONOMETRIC FUNCTIONAL EQUATIONS

  • Published : 2008.10.31

Abstract

In this article we prove the Hyers.Ulam stability of trigonometric functional equations.

Keywords

References

  1. J. Aczel, Lectures on Functional Equations in Several Variables, Academic Press, New York-London, 1966
  2. J. Aczel and J. Dhombres, Functional Equations in Several Variables, Cambridge University Press, New York-Sydney, 1989
  3. J. A. Baker, On a functional equation of Aczel and Chung, Aequationes Math. 46 (1993), 99-111 https://doi.org/10.1007/BF01834001
  4. J. A. Baker, The stability of cosine functional equation, Proc. Amer. Math. Soc. 80 (1980), 411-416 https://doi.org/10.2307/2043730
  5. J. Chung, A distributional version of functional equations and their stabilities, Nonlinear Analysis 62 (2005), 1037-1051 https://doi.org/10.1016/j.na.2005.04.016
  6. J. Chung, Stability of functional equations in the space distributions and hyperfunctions, J. Math. Anal. Appl. 286 (2003), 177-186 https://doi.org/10.1016/S0022-247X(03)00468-2
  7. J. Chung, Distributional method for d'Alembert equation, Arch. Math. 85 (2005), 156-160. https://doi.org/10.1007/s00013-005-1234-0
  8. S. Czerwik, Stability of Functional Equations of Ulam-Hyers-Rassias Type, Hadronic Press, Inc., Palm Harbor, Florida, 2003
  9. D. H. Hyers and Th. M. Rassias, Approximate homomorphisms, Aequationes Math. 44 (1992), 125-153 https://doi.org/10.1007/BF01830975
  10. D. H. Hyers, G. Isac, and Th. M. Rassias, Stability of Functional Equations in Several Variables, Birkhauser, 1998
  11. D. H. Hyers, On the stability of the linear functional equations, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222-224 https://doi.org/10.1073/pnas.27.4.222
  12. S.-M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press, Inc., Palm Harbor, Florida, 2001
  13. K. W. Jun and H. M. Kim, Stability problem for Jensen-type functional equations of cubic mappings, Acta Mathematica Sinica, English Series 22 (2006), no. 6, 1781-1788 https://doi.org/10.1007/s10114-005-0736-9
  14. C. G. Park, Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algabras, Bull. Sci. Math. 132 (2008), 87-96 https://doi.org/10.1016/j.bulsci.2006.07.004
  15. Th. M. Rassias, On the stability of functional equations in Banach spaces, J. Math. Anal. Appl. 251 (2000), 264-284 https://doi.org/10.1006/jmaa.2000.7046
  16. Th. M. Rassias, On the stability of linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300 https://doi.org/10.2307/2042795
  17. L. Szekelyhidi, The stability of sine and cosine functional equations, Proc. Amer. Math. Soc. 110 (1990), 109-115 https://doi.org/10.2307/2048249
  18. S. M. Ulam, A Collection of Mathematical Problems, Interscience Publ., New York, 1960

Cited by

  1. Ulam-Hyers Stability of Trigonometric Functional Equation with Involution vol.2015, 2015, https://doi.org/10.1155/2015/742648
  2. On a Generalized Hyers-Ulam Stability of Trigonometric Functional Equations vol.2012, 2012, https://doi.org/10.1155/2012/610714