Skip to content

Advertisement

  • Research Article
  • Open Access

On the Stability of Trigonometric Functional Equations

Advances in Difference Equations20082007:090405

https://doi.org/10.1155/2007/90405

  • Received: 17 February 2007
  • Accepted: 5 October 2007
  • Published:

Abstract

The aim of this paper is to study the superstability related to the d'Alembert, the Wilson, the sine functional equations for the trigonometric functional equations as follows: .

Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Functional Equation

[123456789]

Authors’ Affiliations

(1)
Department of Mathematics, Kangnam University, Youngin, Gyeonggi, 446-702, South Korea

References

  1. Baker J, Lawrence J, Zorzitto F: The stability of the equation . Proceedings of the American Mathematical Society 1979,74(2):242–246.MATHMathSciNetGoogle Scholar
  2. Bourgin DG: Approximately isometric and multiplicative transformations on continuous function rings. Duke Mathematical Journal 1949,16(2):385–397. 10.1215/S0012-7094-49-01639-7MATHMathSciNetView ArticleGoogle Scholar
  3. Baker JA: The stability of the cosine equation. Proceedings of the American Mathematical Society 1980,80(3):411–416. 10.1090/S0002-9939-1980-0580995-3MATHMathSciNetView ArticleGoogle Scholar
  4. Cholewa PW: The stability of the sine equation. Proceedings of the American Mathematical Society 1983,88(4):631–634. 10.1090/S0002-9939-1983-0702289-8MATHMathSciNetView ArticleGoogle Scholar
  5. Badora R: On the stability of the cosine functional equation. Rocznik Naukowo-Dydaktyczny. Prace Matematyczne 1998, (15):5–14.Google Scholar
  6. Badora R, Ger R: On some trigonometric functional inequalities. In Functional Equations—Results and Advances, Advances in Mathematics. Volume 3. Kluwer Academy, Dordrecht, The Netherlands; 2002:3–15.Google Scholar
  7. Kannappan Pl, Kim GH: On the stability of the generalized cosine functional equations. Annales Acadedmiae Paedagogicae Cracoviensis - Studia Mathematica 2001, 1: 49–58.Google Scholar
  8. Kim GH: The stability of d'Alembert and Jensen type functional equations. Journal of Mathematical Analysis and Applications 2007,325(1):237–248. 10.1016/j.jmaa.2006.01.062MATHMathSciNetView ArticleGoogle Scholar
  9. Kim GH: A stability of the generalized sine functional equations. Journal of Mathematical Analysis and Applications 2007,331(2):886–894. 10.1016/j.jmaa.2006.09.037MATHMathSciNetView ArticleGoogle Scholar

Copyright

Advertisement